Datasets:

tomekkorbak

/

pile-pii-scrubadub

like 4

[ "Skulls 3D Pencil Case\n\n£4.99\n\n(approx. ", "$6.39 or €5.59)\n\nOut of Stock - Product Discontinued\n\nProduct Info\n\nCovered in funky coloured skulls, there's more than meets the eye with this black pencil case! ", "With a 3D effect - much like a holograph - these bold and bright realistic skeleton heads almost seem to pop out! ", "Mix up your stationery in the coolest way possible with this trippy pencil case!" ]

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[ "--- instance0 ---\ngap_advertise\n_IRQ_CENTRAL_CONNECT\n_IRQ_MTU_EXCHANGED 256\ngatts_notify\n_IRQ_GATTS_WRITE\ngatts_read\ncharacteristic len: 253 a\n_IRQ_CENTRAL_DISCONNECT\ngap_advertise\n_IRQ_CENTRAL_CONNECT\n_IRQ_MTU_EXCHANGED 200\ngatts_notify\n_IRQ_GATTS_WRITE\ngatts_read\ncharacteristic len: 197 b\n_IRQ_CENTRAL_DISCONNECT\ngap_advertise\n_IRQ_CENTRAL_CONNECT\n_IRQ_MTU_EXCHANGED 300\ngatts_notify\n_IRQ_GATTS_WRITE\ngatts_read\ncharacteristic len: 297 c\n_IRQ_CENTRAL_DISCONNECT\ngap_advertise\n_IRQ_CENTRAL_CONNECT\n_IRQ_MTU_EXCHANGED 50\ngatts_notify\n_IRQ_GATTS_WRITE\ngatts_read\ncharacteristic len: 47 d\n_IRQ_CENTRAL_DISCONNECT\ngap_advertise\n_IRQ_CENTRAL_CONNECT\ngattc_exchange_mtu\n_IRQ_MTU_EXCHANGED 256\ngatts_notify\n_IRQ_GATTS_WRITE\ngatts_read\ncharacteristic len: 253 e\n_IRQ_CENTRAL_DISCONNECT\ngap_advertise\n_IRQ_CENTRAL_CONNECT\ngattc_exchange_mtu\n_IRQ_MTU_EXCHANGED 190\ngatts_notify\n_IRQ_GATTS_WRITE\ngatts_read\ncharacteristic len: 187 f\n_IRQ_CENTRAL_DISCONNECT\ngap_advertise\n_IRQ_CENTRAL_CONNECT\ngattc_exchange_mtu\n_IRQ_MTU_EXCHANGED 290\ngatts_notify\n_IRQ_GATTS_WRITE\ngatts_read\ncharacteristic len: 287 g\n_IRQ_CENTRAL_DISCONNECT\ngap_advertise\n--- instance1 ---\ngap_connect\n_IRQ_PERIPHERAL_CONNECT\ngattc_exchange_mtu\n_IRQ_MTU_EXCHANGED 256\n_IRQ_GATTC_NOTIFY 64 0\ngattc_discover_characteristics\n_IRQ_GATTC_CHARACTERISTIC_RESULT UUID('00000000-1111-2222-3333-444444444444')\n_IRQ_GATTC_CHARACTERISTIC_DONE\ngattc_write\n_IRQ_GATTC_WRITE_DONE\ngap_disconnect: True\n_IRQ_PERIPHERAL_DISCONNECT\ngap_connect\n_IRQ_PERIPHERAL_CONNECT\ngattc_exchange_mtu\n_IRQ_MTU_EXCHANGED 200\n_IRQ_GATTC_NOTIFY 64 1\ngattc_discover_characteristics\n_IRQ_GATTC_CHARACTERISTIC_RESULT UUID('00000000-1111-2222-3333-444444444444')\n_IRQ_GATTC_CHARACTERISTIC_DONE\ngattc_write\n_IRQ_GATTC_WRITE_DONE\ngap_disconnect: True\n_IRQ_PERIPHERAL_DISCONNECT\ngap_connect\n_IRQ_PERIPHERAL_CONNECT\ngattc_exchange_mtu\n_IRQ_MTU_EXCHANGED 300\n_IRQ_GATTC_NOTIFY 64 2\ngattc_discover_characteristics\n_IRQ_GATTC_CHARACTERISTIC_RESULT UUID('00000000-1111-2222-3333-444444444444')\n_IRQ_GATTC_CHARACTERISTIC_DONE\ngattc_write\n_IRQ_GATTC_WRITE_DONE\ngap_disconnect: True\n_IRQ_PERIPHERAL_DISCONNECT\ngap_connect\n_IRQ_PERIPHERAL_CONNECT\ngattc_exchange_mtu\n_IRQ_MTU_EXCHANGED 50\n_IRQ_GATTC_NOTIFY 47 3\ngattc_discover_characteristics\n_IRQ_GATTC_CHARACTERISTIC_RESULT UUID('00000000-1111-2222-3333-444444444444')\n_IRQ_GATTC_CHARACTERISTIC_DONE\ngattc_write\n_IRQ_GATTC_WRITE_DONE\ngap_disconnect: True\n_IRQ_PERIPHERAL_DISCONNECT\ngap_connect\n_IRQ_PERIPHERAL_CONNECT\n_IRQ_MTU_EXCHANGED 256\n_IRQ_GATTC_NOTIFY 64 4\ngattc_discover_characteristics\n_IRQ_GATTC_CHARACTERISTIC_RESULT UUID('00000000-1111-2222-3333-444444444444')\n_IRQ_GATTC_CHARACTERISTIC_DONE\ngattc_write\n_IRQ_GATTC_WRITE_DONE\ngap_disconnect: True\n_IRQ_PERIPHERAL_DISCONNECT\ngap_connect\n_IRQ_PERIPHERAL_CONNECT\n_IRQ_MTU_EXCHANGED 190\n_IRQ_GATTC_NOTIFY 64 5\ngattc_discover_characteristics\n_IRQ_GATTC_CHARACTERISTIC_RESULT UUID('00000000-1111-2222-3333-444444444444')\n_IRQ_GATTC_CHARACTERISTIC_DONE\ngattc_write\n_IRQ_GATTC_WRITE_DONE\ngap_disconnect: True\n_IRQ_PERIPHERAL_DISCONNECT\ngap_connect\n_IRQ_PERIPHERAL_CONNECT\n_IRQ_MTU_EXCHANGED 290\n_IRQ_GATTC_NOTIFY 64 6\ngattc_discover_characteristics\n_IRQ_GATTC_CHARACTERISTIC_RESULT UUID('00000000-1111-2222-3333-444444444444')\n_IRQ_GATTC_CHARACTERISTIC_DONE\ngattc_write\n_IRQ_GATTC_WRITE_DONE\ngap_disconnect: True\n_IRQ_PERIPHERAL_DISCONNECT\n" ]

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[ "Q:\n\nLink tables with extra column in Symfony 2 / Doctrine\n\nIn a database I have the tables User, Group and UsersInGroup and generate the entities from the database using the Symfony 2 console. ", "The table UsersInGroup is not generated as an entity but is partly generated into User and Group. ", "This would be perfect if UsersInGroup hat only two columns userId and groupId (together primarykey), in this case the table UsersInGroup also contains a third column Role. ", "This field is can never be filled using the generated entities\nHow should I fill the Role column in the tabel UsersInGroup?", "\n\nA:\n\nYou have to declare your relation table manually and to map the relations.", "\nYou'll find an interesting discussion here:\nDoctrine2: Best way to handle many-to-many with extra columns in reference table\n\n" ]

{ "pile_set_name": "StackExchange" }

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[ "1 Million UST Giveaway! ", "YouTube live AMA interview with Crypto Influencer Crypto Crow Usechain Follow Jun 6, 2018 · 1 min read\n\nOn 6th June, 12:00 (EST), Professor Cao will be on a YouTube AMA live interview with Crypto Crow. ", "If you have any questions about Usechain, you can ask Professor Cao directly, and he will answer you everything during the live time. ", "Professor Cao will share details on Usechain project and explain what you really interested.", "\n\nWe’re looking forward to your watching,and we prepared benefits for every qualified viewer. ", "The reward for every qualified viewer will be max to 333 UST, and we will giveaway total 1 million UST!", "\n\nThe live AMA address will be public one hour before the live starts, please pay attention on our Twitter/Facebook/telegram, for more details you can follow our account.", "\n\nReach us at:\n\nWebsite: http://www.usechain.net/\n\nWeibo: https://weibo.com/usechain\n\nTwitter: https://twitter.com/usechain\n\nFacebook: https://www.facebook.com/UsechainFoundation/\n\nTelegram: https://t.me/usechaingroup\n\nMedium: https://medium.com/usechain/\n\nBitcointalk: https://bitcointalk.org/index.php?topic=3432061.0\n\nReddit: https://www.reddit.com/user/Usechain" ]

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[ "//******************************************************************************\n// Copyright (c) 2005-2013 by Jan Van hijfte\n//\n// See the included file COPYING.TXT for details about the copyright.", "\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.", "\n//******************************************************************************\n\n\n#include \"qimagewriter_c.h\"\n\nQImageWriterH QImageWriter_Create()\n{\n\treturn (QImageWriterH) new QImageWriter();\n}\n\nvoid QImageWriter_Destroy(QImageWriterH handle)\n{\n\tdelete (QImageWriter *)handle;\n}\n\nQImageWriterH QImageWriter_Create2(QIODeviceH device, const QByteArrayH format)\n{\n\treturn (QImageWriterH) new QImageWriter((QIODevice*)device, *(const QByteArray*)format);\n}\n\nQImageWriterH QImageWriter_Create3(PWideString fileName, const QByteArrayH format)\n{\n\tQString t_fileName;\n\tcopyPWideStringToQString(fileName, t_fileName);\n\treturn (QImageWriterH) new QImageWriter(t_fileName, *(const QByteArray*)format);\n}\n\nvoid QImageWriter_setFormat(QImageWriterH handle, const QByteArrayH format)\n{\n\t((QImageWriter *)handle)->setFormat(*(const QByteArray*)format);\n}\n\nvoid QImageWriter_format(QImageWriterH handle, QByteArrayH retval)\n{\n\t*(QByteArray *)retval = ((QImageWriter *)handle)->format();\n}\n\nvoid QImageWriter_setDevice(QImageWriterH handle, QIODeviceH device)\n{\n\t((QImageWriter *)handle)->setDevice((QIODevice*)device);\n}\n\nQIODeviceH QImageWriter_device(QImageWriterH handle)\n{\n\treturn (QIODeviceH) ((QImageWriter *)handle)->device();\n}\n\nvoid QImageWriter_setFileName(QImageWriterH handle, PWideString fileName)\n{\n\tQString t_fileName;\n\tcopyPWideStringToQString(fileName, t_fileName);\n\t((QImageWriter *)handle)->setFileName(t_fileName);\n}\n\nvoid QImageWriter_fileName(QImageWriterH handle, PWideString retval)\n{\n\tQString t_retval;\n\tt_retval = ((QImageWriter *)handle)->fileName();\n\tcopyQStringToPWideString(t_retval, retval);\n}\n\nvoid QImageWriter_setQuality(QImageWriterH handle, int quality)\n{\n\t((QImageWriter *)handle)->setQuality(quality);\n}\n\nint QImageWriter_quality(QImageWriterH handle)\n{\n\treturn (int) ((QImageWriter *)handle)->quality();\n}\n\nvoid QImageWriter_setCompression(QImageWriterH handle, int compression)\n{\n\t((QImageWriter *)handle)->setCompression(compression);\n}\n\nint QImageWriter_compression(QImageWriterH handle)\n{\n\treturn (int) ((QImageWriter *)handle)->compression();\n}\n\nvoid QImageWriter_setGamma(QImageWriterH handle, float gamma)\n{\n\t((QImageWriter *)handle)->setGamma(gamma);\n}\n\nfloat QImageWriter_gamma(QImageWriterH handle)\n{\n\treturn (float) ((QImageWriter *)handle)->gamma();\n}\n\nvoid QImageWriter_setDescription(QImageWriterH handle, PWideString description)\n{\n\tQString t_description;\n\tcopyPWideStringToQString(description, t_description);\n\t((QImageWriter *)handle)->setDescription(t_description);\n}\n\nvoid QImageWriter_description(QImageWriterH handle, PWideString retval)\n{\n\tQString t_retval;\n\tt_retval = ((QImageWriter *)handle)->description();\n\tcopyQStringToPWideString(t_retval, retval);\n}\n\nvoid QImageWriter_setText(QImageWriterH handle, PWideString key, PWideString text)\n{\n\tQString t_key;\n\tQString t_text;\n\tcopyPWideStringToQString(key, t_key);\n\tcopyPWideStringToQString(text, t_text);\n\t((QImageWriter *)handle)->setText(t_key, t_text);\n}\n\nbool QImageWriter_canWrite(QImageWriterH handle)\n{\n\treturn (bool) ((QImageWriter *)handle)->canWrite();\n}\n\nbool QImageWriter_write(QImageWriterH handle, const QImageH image)\n{\n\treturn (bool) ((QImageWriter *)handle)->write(*(const QImage*)image);\n}\n\nQImageWriter::ImageWriterError QImageWriter_error(QImageWriterH handle)\n{\n\treturn (QImageWriter::ImageWriterError) ((QImageWriter *)handle)->error();\n}\n\nvoid QImageWriter_errorString(QImageWriterH handle, PWideString retval)\n{\n\tQString t_retval;\n\tt_retval = ((QImageWriter *)handle)->errorString();\n\tcopyQStringToPWideString(t_retval, retval);\n}\n\nbool QImageWriter_supportsOption(QImageWriterH handle, QImageIOHandler::ImageOption option)\n{\n\treturn (bool) ((QImageWriter *)handle)->supportsOption(option);\n}\n\n" ]

{ "pile_set_name": "Github" }

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[ "Q:\n\nParse Cloud Code - How to query the User Class\n\nI'm trying to query the Parse User Class but I'm not getting any results. ", "The User class has a column labeled \"phone\", and I'm passing an array of dictionaries where each dictionary has a key \"phone_numbers\" that corresponds to an array of phone numbers. ", "I'm trying to determine if a User in my table has one of those phone numbers. ", "I'm not getting any errors running the code, but there does exist a user in my table with a matching phone number. ", "What am I doing wrong?", "\nParse.", "Cloud.define(\"hasApp\", function(request, response) {\n var dict = request.params.contacts;\n var num = 0;\n var found = 0;\n var error = 0;\n var phoneNumbers = \"\";\n for (var i = 0; i < dict.length; i++){\n var result = dict[i].phone_numbers;\n num += result.length;\n for (var j = 0; j < result.length; j++){\n phoneNumbers += result[j] + \", \";\n\n var query = new Parse.", "Query(Parse.", "User);\n\n query.equalTo(\"phone\", result[j]);\n query.find({\n success: function(results) {\n found = 1;\n },\n error: function() {\n error = 1;\n }\n });\n }\n }\n response.success(\"hasApp \" + dict.length + \" numbers \" + num + \" found \" + found + \" error \" + error + \" phoneNumbers \" + phoneNumbers);\n});\n\nMy response from calling this is \nhasApp 337 numbers 352 found 0 error 0 phoneNumbers \"list of phone numbers\" \n\nwhere some of those phone numbers appear in my User class. ", "As far as I can tell I'm not getting any errors but I'm also not successfully querying the User table\nUPDATE\nAfter moving \nresponse.success(\"hasApp \" + dict.length + \" numbers \" + num + \" found \" + found + \" error \" + error + \" phoneNumbers \" + phoneNumbers);\n\nto the body of the success block, I get the following error because I'm only allowed to call response.success once per cloud function. ", "\nError Domain=Parse Code=141 \"The operation couldn’t be completed. (", "Parse error 141.)\" ", " \nUserInfo=0x14d035e0 {code=141, error=Error: Can't call success/error multiple times\n at Object.success (<anonymous>:99:13)\n at query.find.success (main.js:44:12)\n at Parse.js:2:5786\n at r (Parse.js:2:4981)\n at Parse.js:2:4531\n at Array.forEach (native)\n at Object.w.each.w.forEach [as _arrayEach] (Parse.js:1:666)\n at n.extend.resolve (Parse.js:2:4482)\n at r (Parse.js:2:5117)\n at Parse.js:2:4531}\n\nDoes this mean that I'm only able to verify one phone number at a time? ", "So I can't pass an array of phone numbers and get the PFUser objects corresponding to those phone numbers (if they exist)?", "\nI understand that my internal query to Parse.", "User is happening synchronously with my \"hasApp\" call, so is there a way to query Parse.", "User asynchronously? ", "That way I can respond back to the client after checking all the phone numbers?", "\n\nA:\n\nYou can use Parse.", "Promise to solve logic where you need to iterate through O(n) number of database queries in one asynchronous Cloud Code definition:\nvar _ = require(\"underscore\"),\n isEmpty = function (o) { // standard function to check for empty objects\n if (o == null) return true;\n if (o.length > 0) return false;\n if (o.length === 0) return true;\n for (var p in o) {\n if (hasOwnProperty.call(o, p)) return false;\n }\n return true;\n };\n\nParse.", "Cloud.define(\"hasApp\", function (request, response) {\n var dict = request.params.contacts,\n users = [];\n\n var promise = Parse.Promise.as();\n _.each(dict, function (obj) {\n _.each(obj.phone_numbers, function (num) {\n promise = promise.then(function () {\n var promiseQuery = new Parse.", "Query(Parse.", "User);\n promiseQuery.equalTo(\"phone\", parseInt(num));\n return promiseQuery.find({\n success: function (result) {\n if (isEmpty(result)) // don't save empty results e.g., \"[]\"\n return;\n users.push(result); // save results to a model to prevent losing it in scope\n }\n });\n });\n });\n });\n return promise.then(function () {\n response.success(\"Found user(s): \" + JSON.stringify(users));\n });\n\n});\n\nNote a few things about this block:\n\nYou can append functionality iteratively to a Parse.", "Promise.", "\nYou can loose scope of database results in your iteration. ", "Use a local array model to save your query results to. ", "Although, I presume there is a better way to achieve the same functionality without the use of a user model, someone else can quote me on that.", "\nPay close attention to the way Parse handles data. ", "For example, if you are storing your phone numbers as numbers, you have to make sure you use parseInt() when querying for it.", "\n\nBe aware that you must attach your response.success() function to your promise to assure it is resolved after your iterations have run. ", "From this block, your response from Parse will look similar to an array of User objects. ", "You can decide on the many different ways you can save the data model depending on what you need it for.", "\nAs a final note, this block doesn't account for any validation or error handling that should be accounted for otherwise.", "\n\n" ]

{ "pile_set_name": "StackExchange" }

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[ "Chalford\n\nChalford is a large village in the Frome Valley of the Cotswolds in Gloucestershire, England. ", "It is to the southeast of Stroud about upstream. ", " It gives its name to Chalford parish, which covers the villages of Chalford, Chalford Hill, France Lynch, Bussage and Brownshill, spread over of the Cotswold countryside. ", "At this point the valley is also called the Golden Valley.", "\n\nGovernance\nAn electoral ward in the same name exists. ", "This ward covers a similar area to the parish but extends to the Brimscombe and Thrupp ward. ", "The total population of the ward taken at the 2011 census was 6,509.", "\n\nHistory \n\nThe remains, and known sites, of many barrows indicate that the plateau area of Chalford Hill, France Lynch and Bussage has been an area of continuous settlement for probably at least 4,000 years. ", "Stone Age flints have been found in the area as well as the remains of a Roman Villa. ", "Several of the place names in the area are also Anglo-Saxon in origin.", "\n\nThe name Chalford may be derived from Calf (Way) Ford, or possibly from the Old English cealj or Chalk and Ford (river crossing point). ", "There were two ancient crossings at Chalford apart from the ford from which the village was named: Stoneford, recorded from the later 12th century, was the crossing-point of a track up Cowcombe hill on the line of the later Cirencester turnpike and by 1413 another track crossed into Minchinhampton by Stephen's bridge at Valley Corner.", "\n\nChalford Hill is a recent title for the western end of the hill: Its original name was Chalford Lynch. \"", "Lynch\" (lynchet in modern English) means a cultivated terrace following the contours of a hill. ", "Chalford Lynch and its extension France Lynch originated in the late 16th century as collections of stone cottages many built illegally on the peripheries of Bisley common as the mill expansion in the valley outstripped accommodation space in the valley. ", "Many dwellings in Franch Lynch and Chalford Hill only became legitimate at the time of the parliamentary enclosures in 1869.", "\n\nThe settling of displaced Flemish Huguenot weavers in the 17th and 18th centuries brought quality silk and woollen cloth manufacturing to the valley. ", "Some say that they gave their name to the neighbouring village of France Lynch. ", "It is more likely that the name comes from a non-conformist chapel, France Meeting that was displaced from the village in the valley to the Lynches above. ", "At this point the Golden Valley is narrow and deep so many weavers' cottages were built clinging to the sides of the hills, giving the village an Alpine air. ", "It is sometimes still referred to as the 'Alpine village'. ", "As the paths on the hillsides were too narrow for more conventional forms of transport donkeys were used to carry groceries and other goods to houses, this tradition continuing until as recently as the 1950s.", "\nChalford expanded rapidly with the opening of the Thames and Severn Canal in 1789 and the village became one of the centres for the manufacture of broadcloth. ", "Its wealthy clothiers lived close to their mills and built many fine houses which survive to this day.", "\n\nArchitecture \n\nIn common with other towns and villages in the area, buildings are generally constructed of Cotswold stone, with local fields enclosed by dry stone walling. ", "The area is designated as an Area of Outstanding Natural Beauty and the village itself is a designated conservation area.", "\n\nChalford is noted for two fine Arts and Crafts movement churches. ", "Christ Church (Church of England) contains work by Norman Jewson, William Simmonds, Peter Waals, Edward Barnsley, Norman Bucknell, amongst other distinguished artists and craftsmen working in the Cotswold tradition. ", "The Church of Our Lady of the Angels (Roman Catholic), Brownshill, by W. D. Caroe (1930), contains outstanding stained glass by Douglas Strachan. ", "France Lynch, part of the civil parish but a separate ecclesiastical parish has a splendid listed church, St John the Baptist, built by George Frederick Bodley who went on to build Washington National Cathedral in Washington DC.", "\n \nOne of the most distinctive, and most photographed, features of the village is the Round House. ", "It was built by the Thames and Severn Canal Company as a lengthman's cottage and is one of five along the Thames and Severn Canal. (", "The others are at Coates, Cerney Wick, Marston Meysey and Inglesham.) ", "A notable feature is that access is by way of steps up to the first floor as the ground floor would have originally been stabling for a horse. ", "Apart from a relatively short break in the 1950s when it was a museum it has fulfilled its function as a private residence, which it continues to do to this day.", "\n\nDirectly opposite the Round House is Chalford Place, a Grade II* listed building built on the site of the original home of the de Chalkfordes who are mentioned in documents as early as 1240. ", "The house, formerly known as the Companys Arms, is one of the earlier houses in the valley. ", "Built as a mill owner's house it became an inn in the 19th century. ", "It owed its name Companys Arms to the East India Company for which the mills of Chalford supplied much of its cloth. ", "It remained an inn until the 1960s when it reverted to its former name of Chalford Place.", "\nThe house lay derelict for many years until it was recently purchased and is now being restored by the artist Damien Hirst\n\nSurviving mills in Chalford parish.", "\n St Mary's Mill\n Clayfields/Ballingers Mill\n Iles Mill\n Belvedere Mill\n Bliss Mills (Bliss, New, Mugmore, Spring and Wood.) ", "Now form Chalford industrial estate.", "\n Woolings Mill (including Sevilles upper mill.)", "\n Smart Mill (formerly known as Stoneford, Bidmeads, Hoptons and Halliday Mill.)", "\n Valley or Morton's Mill\n\nThe mill race of Ashmeads Mill remains, mill demolished early 1900s.", "\n\nNotable former mill owners' houses.", "\n\n Brookside\n Belvedere Mill House\n Chalford Place\n Chestnut House (Smarts Mill House)\n Green Court\n Old Valley Inn (formerly Clothier's Arms)\n Sevilles House\n Springfield House\n St Mary's Mill House\n Vale House\n\nListed buildings\n\n Grade II* : Chalford Place, St John the Baptist, St Mary's House, Wing Cottage\n Grade II : Baptist Chapel, Church of St Michael and All Angels, Christ Church, France Congregational Church and Hall\n\nModern Chalford \n\nIn February 2008, Chalford hit the headlines when a community plan to reintroduce donkeys as a way of carrying shopping up the steep, narrow hills became public.", "\n\nOn 5 September 2009 Chalford Community Stores allowed customers to purchase shares in the business. ", "The store,\nwhich has been running with the aid of a volunteer workforce since 2003, is now affiliated with the independent organisation Co-operatives UK, making the share issue possible. ", "On 4 March 2012 the store and the donkey were featured in an episode of Countryfile. ", "The store prospered within the local church hall but returned to the High Street in May 2014 and now thrives in the former Seventh Day Adventist Hall. ", "This was made possible by a second community share issue which raised in excess of £50,000 alongside a bank loan and various grants.", "\n\nResidents \n\nNotable residents include James Bradley, the third Astronomer Royal, who died in Chalford in 1762, and the 19th-century sculptor John Thomas. ", "Henry Cooper lived in the village as a child, after being evacuated here during the Second World War. ", "The artist Damien Hirst has a studio in the village. ", "Lord Janvrin, former Private Secretary to H.M. the Queen, maintains a house in the village and on his retirement was gazetted as Baron Janvrin of Chalford Hill, on 10 October 2007. ", "The Public Relations guru Mark Borkowski lives at Oakridge.", "\n\nBrownshill\nThe sub-village of Brownshill is home to the Monastery of Our Lady and St Bernard which is home to a community of eight Bernardine Cistercian nuns. ", "There is a sister community at the Monastery of Our Lady of Hyning at Warton, near Carnforth.", "\n\nSt Mary of the Angels is a small Roman Catholic church built at Brownshill in the 1930s with funds from two former nurses, Bertha Kessler and Katherine Hudson. ", "The architect was W. D. Caroe, with windows by Douglas Strachan.", "\n\nThe Golden Valley \n\nThe question of how the Golden Valley acquired its name is sometimes asked.", "\n\nThe first written reference to the Golden Valley is in Rudder's 1779 History of Gloucestershire. (", "It can be assumed that the name pre-dates his recording of it but how far back in unknown other than a reference in Issac Taylor's map dated 1777 - see Point 4 below.)", "\n\nThe Place Names of Gloucestershire, published in 1965 by the University of Cambridge and edited by A H Smith, notes that Rudder's is the first written record and also notes 'doubtless so called from the wealth that came from its industries.' ", "However, there is no substantiation or source for this particular observation. ", "It is also worth noting that Rudder records that a Roger Gulden held lands in the area in the middle Medieval period, therefore it is possible that in fact this is the source of the name as a corruption of the surname.", "\n\nFrom time to time, people will claim that it was Queen Victoria who named the Valley sometime during her reign. ", "This is a myth and she is not responsible for giving this delightful valley the name, which clearly has a significantly longer history. ", "On the other hand she did pass through the Golden Valley twice in the summer and on both occasions made a note in her journals.", "\n\nOn 29 September 1849, Queen Victoria travelled from Gloucester to Swindon by train,\n\n\"Before we came to Gloucester we passed through the beautiful valley of Stroud, so green & hilly, but soon after Swindon, all beauty of scenery faded away.\" (", "So green and not golden.)", "\n\nThree years later on August 30, 1852 she wrote:\n\n\"We passed Reading & at 2 reached Swindon, where we got out & had some luncheon. ", "Left again in less than ½ an hour, & passed by the very pretty & picturesque valley of Stroud, which is full of manufactures scattered about, & this makes one hardly realise, that it is a manufacturing district. ", "After 3 we reached Gloucester, & here we left the Great Western for another line. ", "The Malvern Hills could be distinctly seen in the distance. ", "We stopped at ½ p. 4 at Broomsgrove station, where the Worcestershire Yeomanry, with Mr Clive, their Col: were drawn up, Sir J. Packington & Ld Lyttelton, being also there with their wives, &c.\"\n\nLater in the 19 century the use of the Golden Valley had become common:\n\n1. ", "A Handbook for Travellers in Gloucestershire, Worcestershire, and Herefordshire published 1867 records when describing the rail journey to Stroud 'the traveller is carried along the side of a steep valley, thickly timbered, whose tints in autumn have given it the name the Golden Valley.'", "\n\n2. ", "THE JOURNAL OF HORTICILTURE, COTTAGE GARDENER, COUNTRY GENTLEMAN. ", "BEE-KEEPER ...By GEORGE W.JOHNSON,F.R.H.S. published in Country Life in 1870 refers to the 'golden valley in Stroud and beautiful it is.'", "\n\n3. ", "Paul Hawkins Fisher in his Notes and Recollections of Stroud, published in 1871 describes the Golden Valley and notes that 'in autumn it is all a-glow with the bright golden tints of its beech leaves.'", "\n\nFinally...\n\n4. ", "The Victoria County History for Gloucestershire Vol 11 published in 1976 '..Golden Valley in the south-east part, which had acquired its name by the late 18th century, either from its autumn hues or from the prosperity of the local cloth-mills,' and refers to Issac Taylor's 1777 map of Gloucestershire as a footnote.", "\n\nAny mention of Queen Victoria naming the valley 'golden' is recent, without verification, and seems confined to a few blogs, an article in the Stroud News and Journal, a couple of guide books, and mentions on the radio station BBC Gloucestershire.", "\n\nSee also \n Aston Down airfield across the Golden Valley from Chalford\n\nReferences\n\nExternal links \n\n Chalford Hill\n Chalford Hill - Brief History\n Stroud Voices (Chalford filter) - oral history site\n\nCategory:Villages in Gloucestershire\nCategory:Stroud District\nCategory:Civil parishes in Gloucestershire" ]

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[ "Pic Pic cheats:\n\nThis page contains Pic Pic cheats, hints, walkthroughs and more for Nintendo DS. ", "This game has been made by Success and published by Success at Dec 31, 1969. ", "Pic Pic was made in \"Logic Puzzle\" genre. ", "Right now we have 1 Walkthroughs and etc for this game and every day we increase our collection with new Pic Pic cheats If you can not find the needed cheat in our list, check this page periodically or subscribe for this game's updates!", "\n\nSubmit a cheat!", "\n\nHelp out other Pic Pic players on the Nintendo DS by adding a cheat or secret that you know! ", "Please contribute by clicking this link" ]

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[ "Q:\n\nType Safe Redux Reducer with Arguments\n\nI'm trying to use typescript with react-redux, I'm having some issues with the reducer. ", "With the current setup I'm getting errors but I can't figure out why it's the case. ", "If I deviate from the approach in the redux documentation I am able to get something that works but it's repetitive.", "\n----- CODE: -----\nI have three files in three separate directories which resemble:\nstore\n|_actions\n| |_auth.ts \n|_reducers\n| |_auth.ts\n|_types\n |_actionTypes.ts\n |_auth.ts\n\nwithin actions/auth.ts file:\n// actions/auth.ts\nimport { AuthActionTypes } from '../types/auth';\nimport * as actionTypes from '../types/actionTypes';\n\nexport const authStart = (): AuthActionTypes => {\n return {\n type: actionTypes.", "AUTH_START\n };\n};\n\nexport const authSuccess = ( token: string, userId: string ): AuthActionTypes => {\n return {\n type: actionTypes.", "AUTH_SUCCESS,\n idToken: token,\n userId: userId\n };\n};\n\nexport const authFail = ( error: Error ): AuthActionTypes => {\n return {\n type: actionTypes.", "AUTH_FAIL,\n error: error\n };\n};\n\nthe reducers/auth.ts file:\n// reducers/auth.ts\nimport * as actionTypes from '../types/actionTypes';\nimport { AuthState, AuthActionTypes } from '../types/auth';\nimport { updateObject } from '../utility';\n\nconst initialState: AuthState = {\n token: null,\n userId: null,\n error: null,\n loading: false,\n authRedirectPath: '/'\n};\n\nconst authStart = ( state: AuthState, action: AuthActionTypes ) => {\n return updateObject( state, {error: null, loading: true })\n};\n\nconst authSuccess = ( state: AuthState, action: AuthActionTypes ) => {\n return updateObject( state, { \n token: action.idToken, // ##### this is giving me an error #####\n userId: action.userId, // ##### this is giving me an error #####\n error: null,\n loading: false\n });\n};\n\nconst authFail = ( state: AuthState, action: AuthActionTypes ) => {\n return updateObject( state, {\n error: action.error, // ##### this is giving me an error #####\n loading: false\n });\n};\n\nconst reducer = (state = initialState, action: AuthActionTypes): AuthState => {\n switch (action.type) {\n case actionTypes.", "AUTH_START: return authStart( state, action );\n case actionTypes.", "AUTH_SUCCESS: return authSuccess( state, action );\n case actionTypes.", "AUTH_FAIL: return authFail( state, action );\n default: \n return state;\n };\n};\n\nexport default reducer;\n\nthe types/auth.ts file:\n// types/auth.ts\nimport * as actionTypes from './actionTypes';\n\nexport interface AuthState {\n token: null | string\n userId: null | string\n error: null | Error\n loading: boolean\n authRedirectPath: string\n} \n\ninterface AuthStart {\n type: typeof actionTypes.", "AUTH_START\n}\n\ninterface AuthSuccess {\n type: typeof actionTypes.", "AUTH_SUCCESS;\n idToken: string;\n userId: string;\n}\n\ninterface AuthFail {\n type: typeof actionTypes.", "AUTH_FAIL;\n error: Error;\n}\n\nexport type AuthActionTypes = \n| AuthStart \n| AuthSuccess\n| AuthFail;\n\nfor completeness the updateObject function found in utility.ts file used in reducers/auth.ts\nexport const updateObject = <T, U>(oldObject: T, updatedProperties: U): T => {\n return {\n ...oldObject,\n ...updatedProperties\n };\n};\n\n----- PROBLEM: -----\nWithin reducers/auth.ts the problem lies with the authSuccess arrow function. ", "I am presented with the following error message:\nProperty 'idToken' does not exist on type 'AuthActionTypes'.", "\nProperty 'idToken' does not exist on type 'AuthStart'.", "\n\nWe can see that both idToken and userId are defined in the interface. ", "I don't see why it would be referencing AuthStart and not AuthSuccess. ", "If I export the AuthSucess interface and declare it as the action type for that function then the error message is gone. ", "Is there any way of keeping action as AuthActionType or does it need to be explicitly declared as AuthSucess and the same for the others with this setup?", "\nAdditionaly if I remove all the arrow functions and defined the logic directly in the case the error is no longer there. ", "That is if I have\n// reducers/auth.ts\n...\nconst reducer = (state = initialState, action: AuthActionTypes): AuthState => {\n switch (action.type) {\n ...\n case actionTypes.", "AUTH_SUCCESS: \n return { \n ...state, \n token: action.idToken, \n userId: action.userId, \n error: null,\n };\n...\n\nIs there any way of keeping the setup that I have now without having to but the above logic directly in the swtich case, since the solution I have is easier for me to maintain?", "\n\nA:\n\nConsider the definition of the AuthSuccess function on its own:\nconst authSuccess = ( state: AuthState, action: AuthActionTypes ) => {\n return updateObject( state, { \n token: action.idToken, // ##### this is giving me an error #####\n userId: action.userId, // ##### this is giving me an error #####\n error: null,\n loading: false\n });\n};\n\nThis definition suggests that action can be any of the AuthActionTypes, including AuthStart which lacks the idToken property. ", "Instead type the function as\nconst authSuccess = ( state: AuthState, action: AuthSuccess ) => {\n return updateObject( state, { \n token: action.idToken, // ##### this is giving me an error #####\n userId: action.userId, // ##### this is giving me an error #####\n error: null,\n loading: false\n });\n};\n\nThe switch statement in your reducer will allow typescript to refine the type of action passed to authSuccess as only AuthSuccess and not one of the other AuthActionTypes.", "\nThis is the reason why inlining these functions works fine - the complier knows the action must be of type AuthSuccess in the case block so idToken and userId are valid.", "\n\n" ]

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[ "Żdżarka\n\nŻdżarka is a village in the administrative district of Gmina Hańsk, within Włodawa County, Lublin Voivodeship, in eastern Poland. ", "It lies approximately north of Hańsk, south-west of Włodawa, and east of the regional capital Lublin.", "\n\nReferences\n\nCategory:Villages in Włodawa County" ]

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[ "Coastal resource complexes of South India: options for sustainable management.", "\nIndia's coastal resource complexes were traditionally characterized by a continuum of 'common property resources' or 'commons' that stretched from the shores to the seas. ", "The continuum aided the existence of sustainable livelihood systems for local communities. ", "Today, fragmented policy approaches and economic welfare schemes have caused the disintegration of community control over the continuum. ", "As a consequence, livelihood systems of local communities have declined. ", "The introduction of coastal management guidelines in the 1990s has exacerbated the situation. ", "With reference to a coastal village located in the State of Kerala in South West India, the paper describes the trajectory of unsustainable change that has taken place in the coastal area resource complexes of the country. ", "The paper argues for restoring the continuum of commons in the study area through community driven systems of natural resource management that are based on networks of nested institutions." ]

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[ "Operation Septentrion\n\nOperation Septentrion was a 36-hour military operation of the International Security Assistance Force (ISAF), a NATO-led security mission, that took place December 16–18, 2009, in the Uzbin Valley of eastern Afghanistan.", "\n\nA part of the War in Afghanistan, it involved a force of 1,100 troops, including 750 or 800 members of the French Foreign Legion, 200 United States Special Forces and Afghan National Army (ANA) soldiers.", "\n\nBackground\nSixteen months before the operation, the Uzbin Valley ambush, on August 18, 2008, by the Taliban in the area of Surobi, Afghanistan, had killed ten French soldiers and wounded twenty-one.", "\n\nGoals\nThe operation's purpose was \"reaffirming the sovereignty of Afghan security forces in the north of the Uzbeen Valley\", according to a French military spokesperson, as well as to plant the Afghan flag in what was called a key strategic village. (", "While 75 percent of the Uzbin Valley had been under ISAF control, the rest of the valley had been under the control of the Taliban.)", "\n\nFighting\nDuring more than 90 minutes of combat, several US soldiers were wounded, including three serious injuries. ", "The Taliban fighters attacked with rocket-propelled grenades, mortars and heavy machine gun fire; for the coalition forces, the French troops used shells, backed up by French Tigre and US Apache helicopters and fighter jets. ", "At least one Taliban fighter was killed and three were injured, according to Lieutenant-Colonel Hervé Wallerand, who led the operation.", "\n\nStrategy\nThe French employed what was called the \"Mikado strategy\" (la stratégie du Mikado), after the game Mikado (known in North America as \"pick-up sticks\"), because of the need to plan every move carefully with constant awareness that one wrong step could risk everything being lost. ", "In particular, the Mikado strategy emphasizes consulting with local inhabitants in a shura (or consultation) to minimize the risk of local civilians conspiring against the ANA and ISAF forces. ", "For this reason the operation was preceded by \"weeks of negotiations with local villagers\", according to the BBC News.", "\n\nAftermath\nIn July 2011, the Croix de la Valeur Militaire (\"cross of military valour\"), a French military decoration, was presented to five Americans – Cpt. ", "Thomas Harper, Master Sgt. ", "David Nuemer, Sgt. ", "1st Class Ryan Ahern, Staff Sgt. ", "Casey Roberts and Sgt. ", "Ryan Meister – for their service during the operation.", "\n\nSee also\n\n 2009 in Afghanistan\n Coalition combat operations in Afghanistan in 2009\n Groupement tactique interarmes de Surobi\n\nReferences\n\nExternal links\n Operation Septentrion video (requires Lightbox video). ", "French Ministry of Defense.", "\n\nCategory:2009 in Afghanistan\nCategory:Military operations of the War in Afghanistan (2001–present) involving France\nCategory:Military operations of the War in Afghanistan (2001–present) involving the United States\nCategory:NATO operations in Afghanistan\nCategory:Recipients of the Cross for Military Valour" ]

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[ "\n153 F.Supp. ", "365 (1957)\nHelen P. MARAGON\nv.\nThe UNITED STATES.", "\nNo. ", "530-53.", "\nUnited States Court of Claims.", "\nJuly 12, 1957.", "\nEllsworth T. Simpson, Washington, D. C., for plaintiff.", "\nHarold S. Larsen, Washington, D. C., with whom was Asst. ", "Atty. ", "Gen. Charles K. Rice, for defendant.", "\nJames P. Garland and Gilbert E. Andrews, Jr., Washington, D. C., were on the briefs.", "\nBefore JONES, Chief Judge, and LITTLETON, WHITAKER, MADDEN and LARAMORE, Judges.", "\nLITTLETON, Judge.", "\nIn this case the defendant in 1953 withheld an overpayment of tax of $189.45 by one taxpayer for 1951 and credited it against a deficiency of another taxpayer for 1944. ", "As shown in the findings plaintiff and her husband, John F. Maragon, filed separate individual income tax returns for 1944. ", "Plaintiff paid the tax due by her for 1944, but a deficiency was determined with reference to the separate tax return and liability of John F. Maragon for 1944.", "\nWe think under the facts that it is obvious that this plaintiff, a separate taxpayer, was not liable for the payment of the deficiency determined in respect of the tax of John F. Maragon for 1944. ", "Section 3797(a) (14), 26 United States Code, 1952 ed., ", "provides that \"The term `taxpayer' means any person subject to a tax imposed by this title.\" ", "By paying and fully discharging her separate tax *366 liability for 1944, plaintiff fully met the requirement of this section and we know of no provision of law that would make her liable for the tax for 1944 of a separate taxpayer. ", "Counsel for defendant argues, however, that under the provisions of section 51(b) (1), Title 26 United States Code, 1952 ed., ", "plaintiff is liable for the 1944 deficiency of her husband, John F. Maragon, because for the year 1951 she filed a joint return, including therein her husband, who had no gross income for that year. ", "This section provides:\n\"A husband and wife may make a single return jointly. ", "Such a return may be made even though one of the spouses has neither gross income nor deductions. ", "If a joint return is made the tax shall be computed on the aggregate income and the liability with respect to the tax shall be joint and several.\"", "\nIt will be noted that the phrase \"liability with respect to the tax\" in this section has reference to the joint and several \"liability\" to the Government only with respect to the tax shown on the joint return, and not to a separate liability on a separate return for another year. ", "The same is true with respect to refunds under 26 U.S.C., 1952, ed. § ", "322 (a) (1).[1] Plaintiff was clearly \"the taxpayer\" for 1951 so far as the year 1944 was concerned. ", "She was not \"the taxpayer\" on the separate return of John F. Maragon for 1944.", "\nIn this case the defendant's tax withholding from plaintiff's salary for 1951 (the only year for which she filed a joint return) was $518.92, and her tax liability on her salary was only $329.47. ", "Her tax was, therefore, overpaid by $189.45. ", "The defendant illegally applied this amount in payment of a tax for 1944 for which plaintiff was not legally liable.", "\nThis court held in Hart Glass Manufacturing Co. v. United States, 48 F.2d 435, 73 Ct.", "Cl. ", "32, 43, that the Commissioner was not authorized by law to apply an overpayment of one taxpayer for 1918 to the payment of taxes due by another corporation for that year. ", "In our opinion his action in the present case was illegal. ", "In Philadelphia Rapid Transit Company v. United States, 10 F.Supp. ", "591, 81 Ct.", "Cl. ", "289, cert. ", "denied, 300 U.S. 664, 57 S.Ct. ", "507, 81 L.Ed. ", "872, we held that the Commissioner acted illegally and without authority when he applied an overpayment of tax by a corporate lessee as a credit against a tax due from the lessor corporation, notwithstanding a contractual obligation of lessee corporation to pay taxes assessed against the lessor, since lessee was not \"the taxpayer\" within the meaning of the statute permitting credit of an overpayment against a deficiency.", "\nWe are not here concerned with community property laws of certain States which give a wife a vested one-half undivided interest in the income of her husband and vice versa, such as the laws of the State of Texas. ", "See Clayton v. United States, 44 F.2d 427, 70 Ct.", "Cl. ", "740, and Lattimore et al. ", "v. United States, 12 F.Supp. ", "895, 82 Ct.", "Cl. ", "97, 130, which involved joint returns and credits for the same year.", "\nSection 12(d) of the Internal Revenue Code of 1939, as amended by section 301 of the Revenue Act of 1948, 26 U.S.C. § 12(d), has no application to this case since the income of plaintiff was not community property by the law of the jurisdiction, and the credit was not for 1951.", "\nPlaintiff is entitled to recover $189.45, with interest as provided by law from March 15, 1952.", "\nIt is so ordered.", "\nJONES, Chief Judge, and LARAMORE, Judge, concur.", "\nMADDEN and WHITAKER, Judges, dissent.", "\nNOTES\n[1] \"Overpayment. ", "Where there has been an overpayment of any tax imposed by this chapter, the amount of such overpayment shall be credited against any income, war-profits, or excess-profits tax or installment thereof then due from the taxpayer, and any balance shall be refunded immediately to the taxpayer.\"", "\n" ]

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[ "casebolt wrote:The \"Glory Device\" is a renamed weapon system once apon a time called the \"Wild Weasle\" its a copy right thing.", "\nThe \"Wild Weasle\" was a modified shuttle armed with missles that when triggered launched. ", "The shuttle would get as close to the intended target and overwelm the enemy ship with missles, it was crude but effective.", "\n\nIMO 1-Modify the POP ship make it with Trans Gav engines to outrun normal ship speed, Missles were a primary weapon system of Klingons.", "\n\n2-inhance the targeting system, so as NOT to harm Allies in fleet actions.", "\n\n3- Give the Klingons real Glory, reward them of PBPs.", "\n\nIf not the above then Modify the Victorious with more mass and a 10 beam, 10 torp arms, with the cost of more minerals/MCs.", "\n\nSFB Wild Weasel? (", "Cluster pack?) ", "in VGAP for Klingons only?", "\nIIRC, the Wild Weasel was the decoy for incoming plasma weapons or\ndrones and the Cluster Pack was what you're talking about.", "\n\nGA the thing?", "\n\nI want!", "\n\nUnderstanding is a three-edged sword.", "Your side, their side,and the truth.", "\n\nOne thing that I have created and works and as soon as I get out of here, I will send it to Havok. ", "Is using the intercept mission on the Sabre class ships, and instead of pop or trg, you use the ship ID of a target vessel. ", "A Sabre set to intercept ship1 and has a FC set to 001, the Sabre will then explode at the end of movement. ", "If Ship1 is NOT at the same x,y at the end of movement the Sabre doesn't explode.", "\nSabre looks alot like this.", "\nTri....Dur...Mol....Fuel....Crew....Eng...Mass..Tech..Cargo...Cost..Fb..Tt..Bm\n100...40.....60.....300.....420......2......200......9.......50.......200...0...4...8\n\nSome people spend an entire lifetime wondering if they made a difference.", "\nThe US Marines don't have that problem.", "\nPresident Ronald Reagan\n\nI do like the the GA as a fix and it does match closely to Klingon tactics of\nWarfare. ", "This was very Klingon.", "\n\nOnce the the Glory device is launched \"GA\" it explodes at the end of movement not to be used again, this must be factored into the launch.", "\nThis would give Klingons more teeth rather than depend on Politics that useally is a must for them.", "\n\nWhy any damage to launching race? ", "damageing your own ship with a direct fireing weapon makes no sense. ", "Bleed through damage is so small what is the point. ", "Klingons have to pack extra supplies in their cargo to defend against their own weapons is just plain silly. ", "Free the Klingons up to use less supplies for damage from their own weapons to add more cargo space for Troops, Torps, supplies for colonization.", "\n\nShardin5 wrote:One thing that I have created and works and as soon as I get out of here, I will send it to Havok. ", "Is using the intercept mission on the Sabre class ships, and instead of pop or trg, you use the ship ID of a target vessel. ", "A Sabre set to intercept ship1 and has a FC set to 001, the Sabre will then explode at the end of movement. ", "If Ship1 is NOT at the same x,y at the end of movement the Sabre doesn't explode.", "\n\nThis means the sabre goes to combat with a knowing FC?", "\n\nWhy do you need to reconstruct the Saber? ", "You can reconstruct painmaker for it instead. ", "Its easy to turn painmaker into saber (or nefarious) at the moment it explode.(in Auxbc Phase).", "\nBut i like the idea. ", "How about to use the fc=lfm : if the glory ship ends movement with any non-cloacked enemy ship (kill or PE except alliance) then it explode?", "\n\nShardin5 wrote:One thing that I have created and works and as soon as I get out of here, I will send it to Havok. ", "Is using the intercept mission on the Sabre class ships, and instead of pop or trg, you use the ship ID of a target vessel. ", "A Sabre set to intercept ship1 and has a FC set to 001, the Sabre will then explode at the end of movement. ", "If Ship1 is NOT at the same x,y at the end of movement the Sabre doesn't explode.", "\n\nThis means the sabre goes to combat with a knowing FC?", "\n\nWhy do you need to reconstruct the Saber? ", "You can reconstruct painmaker for it instead. ", "Its easy to turn painmaker into saber (or nefarious) at the moment it explode.(in Auxbc Phase).", "\nBut i like the idea. ", "How about to use the fc=lfm : if the glory ship ends movement with any non-cloacked enemy ship (kill or PE except alliance) then it explode?", "\n\nNot really a known FC at all, and it wouldn't be a big deal if the enemy guessed which ship the Sabre was trying to intercept. ", "Sabre's and D19's are already setup to handle cloakers pretty easily and effectively. ", "Biggest issue is sending a Popper to hit a ship that ends up NOT being at the same x,y at the end of movement and the Klingon ends up waisting a ship in the process. ", "By using the Intercept mission and a FC of the ship that the Klingon wants to hit the Sabre with will ensure that the Sabre only Explodes if that target ship is at the x,y. No Klingon Capt would explode his ship in the ulitmate act of glory and not take any enemies with him.", "\n\nGranted the Sabre couild end up at the end of movement and have to fight, and \"if\" the enemy figured out which ship the Klingon was going to intercept, and the enemy wanted to match that FC to avoid combat on ships that he didn't want to fight, not the end of the world. ", "If the Sabre ended up over a planet with a SB, still not an issue as Surrender happens the beginning of the next turn, so the any decent Klingon Capt will change his FC and move off, or just explode were he is at, and not have to worry about being captured.", "\n\nThats why the Sabre will look like this.", "\nTri....Dur...Mol....Fuel....Crew....Eng...Mass..Tech..Cargo...Cost..Fb..Tt..Bm\n100...40.....60.....300.....420......2......200......9.......50.......200...0...4...8\n\nSome people spend an entire lifetime wondering if they made a difference.", "\nThe US Marines don't have that problem.", "\nPresident Ronald Reagan" ]

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[ "Taoiseach Leo Varadkar has said that he expects the provisions of the backstop, including customs checks at Northern Ireland ports, will be put in place in the event of a no-deal Brexit.", "\n\nThe UK will crash out of the European Union without a deal on April 12th unless it can somehow get the backing of Theresa May’s withdrawal agreement or secure a further delay. ", "Theresa May has requested an extension until June 30th, but this needs the backing of all 27 member states.", "\n\nIf the UK leaves without a deal, the Border in Ireland will become the only land frontier between the EU and the UK a scenario that raises the prospect of a return of physical border infrastructure.", "\n\nMr Varadkar said the “logical” way to ensure a free-flowing Border would be for regulatory checks to take place between Great Britain and Northern Ireland at the ports in Belfast and Larne.", "\n\nMr Varadkar believes Britain will treat Northern Ireland differently as it has said it would do when it announced its tariff regimes last month. ", "In the event of a no-deal Brexit, the British government said there would be no tariffs on goods arriving from the Republic and remaining in Northern Ireland.", "\n\nSpeaking on RTÉ’s Countrywide programme, Mr Varadkar said: “Even in the event of no-deal, we will still be saying to the British that you still have obligations under the Good Friday Agreement.", "\n\n“You committed to full regulatory alignment back in December 2017 and we still want the arrangements in the backstop to apply.”", "\n\nMr Varadkar continued to defend the backstop which was included in the UK’s Withdrawal Agreement but has been rejected by the Democratic Unionist Party (DUP) because it will mean Northern Ireland will continue to be part of the customs union while other parts of the UK will not. ", "This measure would see fierce opposition from unionists who would view it as treating Northern Ireland differently to other parts of the United Kingdom because it would effectively create a border down the Irish sea.", "\n\nBREXIT: The Facts Read them here\n\nThe backstop is an insurance policy that would keep the Border open in the even of no trade agreement being reached during the transition period contained in the the Withdrawal Agreement.", "\n\nWhen questioned as to how a hard Border can be avoided in the event of a no-deal Brexit next Friday, Mr Varadkar said any arrangements which immediately follow on from that would be temporary.", "\n\nHe added: “The UK has already suggested in its no deal planning that it would treat Northern Ireland differently from Great Britain and that opens up the potential to have checks at Larne and Belfast which is the logical place to have them of course and not on the land border,” he explained.", "\n\n“There is a reason why we had the backstop. ", "We did think about all of this already.”", "\n\nExtension\n\nMr Varadkar envisaged that none of the 27 EU countries will object to a further extension as requested by British prime minister Theresa May this week.", "\n\nHe said the European Council operates by consensus and in his two years of attending European Council meetings no country has used the veto.", "\n\nMany member states were frustrated, he suggested, by the time that Brexit was taking up especially among countries that will not be badly affected by it. ", "However, he added that all understood the potential impact of Brexit on Ireland and countries such as France and the Netherlands.", "\n\nMr Varadkar believed that any European leader who exercised his or her veto would not be forgiven for it.", "\n\n“They would know that they would find themselves on the end of that particular veto power in future. ", "It is extremely unlikely that I could see any country vetoing it,” he said.", "\n\n“The likelihood is a further extension, but we want to avoid an extension which allows for more indecision and uncertainty. ", "I would prefer to see a longer extension so the UK could have time to decide what future relationship it would have with the European Union rather than the alternative which could be rolling extensions.”", "\n\nHe suggested his own preference was for a longer extension than the June 30th date proposed by the UK.", "\n\nHe also revealed that if Britain is granted a longer extension and takes part in European elections there will need to be two counts in the European elections in both the Dublin and Ireland South constituencies.", "\n\nIreland has been allocated two extra seats following the redistribution of the UK’s seats once the country voted for Brexit.", "\n\nIt was not envisaged that Britain would still be a member of the EU at the time of the 2019 European elections which means that the last MEPs elected in both constituencies will not be able to take up their seats until Britain finally leaves.", "\n\nThis will necessitate two counts. ", "In Dublin it will mean counting for three seats and then separately for four. ", "In Ireland south it will mean counting for four seats and then separately for five." ]

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[ "Hangzhou Haichao chain factory established in 1994,is one of special manufacters of industial chains in China, Haichao’s main products include roller chain A series and B series, conveyor chains, special chains,connecting link (04C-56B,03A-240) offset link(04C-56B,03A-240) , and we can provide sprockets, pulleys, bushes, racks.", "\n\nYong Chao Brand chain used CAD to design and produce chains, its productions conform to the international standard:ISO, DIN,ANSI with advance technology and strict quality examination, its high quality\nand excellect service is welcomed by customers." ]

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[ "---\nabstract: 'A systematic study of two particle correlations measured by the NA49 experiment is summarized. ", "Radii from Bose Einstein interferometry have been determined separately in different parts of phase space, for different collision systems and at different incident beam energies. ", "Moreover, first results of a new method of accessing space-time asymmetries in the emission of particles by means of non identical particle correlations are presented.'", "\naddress: 'Max-Planck-Institut für Physik, Föhringer Ring 6, D-80805 München, Germany'\nauthor:\n- 'R.Ganz for the NA49 collaboration'\ntitle: A systematic study of two particle correlations from NA49 at CERN SPS\n---\n\nBose Einstein Interferometry {#bose-einstein-interferometry .unnumbered}\n----------------------------\n\nThe aim of studying two particle correlations is the reconstruction of the freeze out conditions of final state particles. ", "In relativistic heavy ion collisions it appears that this state has to be described by a set of rather complicated non-isotropic, non-static and particle-type dependent emission functions. ", "To constrain these one has to gather selective information over a wide region of phase space by applying different analysis methods and by a systematic change of the initial condition of the collision. ", "The NA49 experiment [@NIM99] with its four large volume TPCs detecting over 60% of all pions emitted has collected rather a comprehensive body of data. ", "It comprises centrality selected Pb$+$Pb collisions at 158 and at 40 AGeV, minimium bias Pb$+$Pb events at 158 AGeV as well as 158 AGeV p$+$p and p$+$Pb interactions. ", "Overall this represents an ideal basis for such a study. ", "Usually freeze out condition are investigated by means of intensity interferometry which exploits correlations at small momentum differences $Q$ of two particles arising from quantum interference in the case of the two particles being indistinguishable. ", "The description of the correlation function $C_2(Q)$ by a gaussian parametrization in the three components of the momentum difference $Q_{\\mathrm{side}}$, $Q_{\\mathrm{out}}$, $Q_{\\mathrm{long}}$ relates the gaussian width parameters to the transverse ($R_{\\mathrm{side}}$) longitudinal ($R_{\\mathrm{long}}$) and temporal ($R^2_{\\mathrm{diff}}=R^2_{\\mathrm{out}}-R^2_{\\mathrm{side}}$) extent of the source at freeze out. ", "In order to observe the mere quantum statistical interference of like sign charged pions the correlation function has to be corrected for correlations owing to final state interactions mainly due to the Coulomb repulsion. ", "For our central Pb$+$Pb 158 AGeV data this correction is done – as described in [@NA35Coul] – by the measured correlation function of unlike sign charged pairs.", "\n\nIn the case of the minimum bias data sample as well as in case of the central 40 AGeV data analysis the analytical ansatz of the Coulomb correlation, as suggested in [@Led98], is chosen instead. ", "It was incorporated in the fitting procedure of the uncorrected correlation function, to take the size dependence of the Coulomb effect properly into account. ", "Despite the two different methods the results obtained from the central 158 AGeV data sample coincide with those from the most central of five bins [@Glenn] in the minimum bias 158 AGeV data. ", "Due to the expected small source size the usual Gamov factor is applied in case of p$+$p and p$+$Pb collisions to correct for Coulomb correlations, noting that compared to the uncorrected case no significant change of the radii is observed. ", "To eliminate the inefficiency of the NA49 TPCs for detecting pairs of two close tracks, those with distances of less than 2 cm in the Pb$+$Pb analysis or those with relative laboratoy momenta $Q_{\\mathrm{x,y}}<20$ MeV/c and $Q_{\\mathrm{z}}<100$ MeV/c (z beam axis) in the p$+$p and p$+$Pb have been excluded from the analysis. ", "This restriction is imposed on pairs of particles from the same event (corr) as well as on those combined from different events (mix). ", "The latter are used as reference sample (denominator) in the correlation function $C_2= N^{\\mathrm{pair}}_{\\mathrm{corr}}/N^{\\mathrm{pair}}_{\\mathrm{mix}}$. All results presented here refer to the Longitudinal Co-Moving System (LCMS) as the Lorentz frame, which is determined for each pair in such a way that the sum of the longitudinal momentum components of the pair vanishes.", "\n\nResults of the analysis of the p$+$p collisions are shown in the two left columns of figure \\[fig:pppAAA\\] together with results from the analysis of central (CMD$\\ge$7)[^1] and peripheral (CMD$<$7) p$+$Pb collisions. ", "The phase space is subdivided into two regions of the average rapidity $y_{\\pi\\pi}$ of the two pions at $y_{\\pi\\pi} = 3.9$ and into two of the average pion transverse momentum $k_{\\mathrm{t}}$ at $k_{\\mathrm{t}}= 0.25$ GeV$/$c. ", "In each column of figure \\[fig:pppAAA\\] $<y_{\\pi\\pi}>$ is the average over all pairs contributing to the respective region. ", "Similarily $<k_{\\mathrm{t}}>$ are used as abscissae. ", "To increase the statistical significance the distributions from pairs of negative hadrons are added to those of positive hadrons since the separate analyses agree within errorbars. ", "It should be emphasized that for these collision systems this is the first time such a phase space dependent three dimensional analysis has become feasible. ", "The radii from p$+$Pb tend to be slightly larger than those from p$+$p. ", "In all cases an ordering is observed $R_{\\mathrm{long}}>$$R_{\\mathrm{out}}>$$R_{\\mathrm{side}}$, the latter being consistent with the observation of a finite duration of freeze-out. ", "Moreover, the p$+$p radii at large values of k$_{\\mathrm{t}}$ appear to be smaller than those at low k$_{\\mathrm{t}}$. Whereas in central Pb$+$Pb reactions (two right columns of figure \\[fig:pppAAA\\]) such a behaviour of the transverse radii is attributed to a hydrodynamical expansion of the system [@NA49exp] in p$+$p it seems more likely to be a characteristics of the decay pattern of resonances such as the $\\rho$ which play an important role at this shorter length scale.", "\n\nComplementary to the change of the collision system is the variation in centrality of the collision. ", "In the right column of figure \\[fig:centrality\\] the dependence on the number $n_{\\mathrm{part}}$ of nucleons participating in the collision is shown for Pb$+$Pb collisions at different centralities accompanied by our p$+$p result and by the NA35 result in the system S$+$S at 200 AGeV. With increasing $n_{\\mathrm{part}}$ the transverse radii $R_{\\mathrm{out}}$ and $R_{\\mathrm{side}}$ grow continously whereas $R_{\\mathrm{long}}$ appears constant. ", "$R^2_{\\mathrm{diff}}$ is positive over the full range and $R_{\\mathrm{diff}}$ grows linearly with $n_{\\mathrm{part}}$. Similar to the findings of NA35 [@NA35SS] RQMD gives a good agreement for $R_{\\mathrm{side}}$ but overestimates $R_{\\mathrm{out}}$ and $R_{\\mathrm{long}}$. A comparison of $R_{\\mathrm{side}}$ with an estimate of the geometrical transverse size of the overlap region in the collsions (figure \\[fig:centrality\\] line[^2]) demonstrates that the interferometric radii reflect the freeze-out stage which is preceeded by a strong expansion of the dense collision zone produced shortly after the collision [@NA49exp]. ", "The left column of figure \\[fig:centrality\\] shows a first step towards closing the gap between the highest AGS energy at 11.6 AGeV and the SPS measurements at 158 AGeV by the (very preliminary) results from the 40 AGeV commissioning run of NA49 in 1998. ", "Although the 40 AGeV and the 158 AGeV results are taken at $\\frac{<y_{\\mathrm{\\pi\\pi}}> - y_{\\mathrm{cms}}}{y_{\\mathrm{cms}}}\n\\approx 1.0$ whereas the AGS point [@E866] is measured at mid-rapidity, the comparison is justified by the observed slow variation of the the radii with $y_{\\mathrm{\\pi\\pi}}$ in NA49. ", "In the transition from AGS to the highest SPS energy $R_{\\mathrm{long}}$ more than doubles whereas a small increase in the transverse radii $R_{\\mathrm{out}}$ and $R_{\\mathrm{side}}$ is observed and the temporal component $R_{\\mathrm{diff}}$ even seems to be a constant.", "\n\nCorrelations of Non Identical Particles {#correlations-of-non-identical-particles .unnumbered}\n---------------------------------------\n\nA method for investigating space-time emission asymmetries has been suggested in [@Led96], which utilizes the effects of final state interaction on the correlations of two non identical particles at small relative velocities. ", "Contrary to the BE correlation method it gives access to the space-time asymmetries in the emission function of different particle species. ", "Such an analysis was carried out for the first time in the SPS energy regime and is presented here for the case of proton-pion correlations. ", "The method involves the correlation functions $C_+(Q_{\\mathrm{inv}})$ and $C_-(Q_{\\mathrm{inv}})$ derived for the two cases where $\\cos\\Psi>0$ and $\\cos\\Psi<0$, respectively, with $\\Psi$ being defined as the angle between the pair velocity sum-vector and the velocity difference-vector in the rest frame of the pair and $Q_{\\mathrm{inv}}$ redefined as the momentum difference in the pair rest frame[^3]. ", "A deviation of the ratio $\\frac{C_+}{C_-}(Q_{\\mathrm{inv}})$ from unity then allows – besides a more quantitative evaluation – for a distinction of emission patterns, for which on the one hand (I) low $p_t$ pions are emitted later or/and closer to the reaction axis and on the other hand (II) low $p_t$ pions are emitted earlier or/and further from the reaction axis than high $p_t$ protons. ", "Results for a small subset of NA49 data of about 40.000 central Pb$+$Pb events are shown in figure \\[fig:nonid\\]. ", "The data clearly exhibit asymmetries in the space-time emission favouring scenario I of the above two. ", "Moreover, a good agreement is achieved in comparison to RQMD 2.3, in which the spatial component plays the dominant role in the occurance of the asymmetry observed for the model.", "\n\n[9]{} S. Afanasiev et al., ", "NIM A430(1999)210 and F. Sikler for NA49, this proceedings. ", "T. Alber et al., ", "Z. Phys.", " C73(1997)443 Y. M. Sinyukov et al., ", "Phys.", " Lett.", " B432(1998) 417. ", "G. Cooper for NA49, this proceedings. ", "H. Appelshäuser et al., ", "Euro.", " Phys.", " Jour.", " C2(1998) 611. ", "R. Soltz for E866, this proceedings. ", "T. Alber et al., ", "Phys.", " Rev. Lett.", " 74(1995) 1303 and Nucl.", " Phys. ", "A590(1995) 453. ", "R. Lednicky et al., ", "Phys.", " Lett.", " B371(1996) 30.", "\n\n[^1]: For a definition of CMD see the contribution [@Glenn] to this conference.", "\n\n[^2]: The line in $R_{\\mathrm{side}}$ corresponds to the average distance of points in the overlap region of two spheres of radius $1.16 A^{1/3}$ offset by the impact paramter from the center of the the collision, projected into a randomly oriented reaction plane.", "\n\n[^3]: In this frame $Q_{\\mathrm{inv}}$ is equal to the relative velocity times the reduced mass of the pair. ", "For pairs of equal mass particles the definition coincides with the usual definition of $Q_{\\mathrm{inv}}$.\n" ]

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[ "Value For Money\n\nGuest's review of Bob Martin Flea Kill\n\nI BOUGHT BOB MARTINS PIPETTS FOR FLEAS FROM MORROSONS BLACKBURN THE SMALL DOG TREATMEN WAS 1POUND 98 DEARER THAN THE BIG DOGS TREATMENT I THINK THIS IS TOTALY WRONG YOU USR A LOWER STRENGTH FOR SMALL BREEDS WUY IS IT MORE EXPENSIVE I DO LIKE THE PRODUCT BUT FINED IT CONFUSING I ALSO BUY THE CAT VERSION WHY DO WE GAT THREE PIPS AND ONLY ONE DOG" ]

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[ "Q:\n\nProgram win32 installer from scratch\n\nI want to recreate a basic Windows installer, like the ones nullsoft or innosetup produce, but in Java.", "\nUnfortunatly, I'm a bit lost for some points.", "\nFirst of all I'd have to copy the software data to Program Files, this point seems clear to me. ", "But I suppose that I would also have to send some information to the OS, for instance to have my program's uninstaller listed in the Programs and Features part of the Control Panel.", "\nAnd I also need to create some icons on the desktop and put an entry on start menu.", "\nThere are probably a ton of other things I forgot, so what are they, and what is the best way to do these in java ?", "\n\nA:\n\nTake a look at IzPack, I think is what you are looking for ...\nIf you don't like it as it is, you can take a look at the source code at the official git repo.", "\n\n" ]

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[ "Long-term Effects of Disasters on Health Care Utilization: Hurricane Katrina and Older Individuals with Diabetes.", "\nWhile the short-term effects of disasters on health care utilization are well documented, less is known regarding potential longer-term effects. ", "This study investigates the effects of Hurricane Katrina on the health care utilization of older individuals with diabetes. ", "We examined Medicare claims and enrollment data for the 2002-2004 and 2006-2008 time periods for older individuals with diabetes. ", "Our quasi-experimental design analyzed utilization across 2 treated and 3 control groups. ", "We compared the proportion of individuals who received a screen related to diabetes before and after Katrina in the treated groups to the proportions in the control groups. ", "Our regression analysis employs individual and year fixed effects to control for factors specific to a given individual or to a given year. ", "We found that utilization rates in the 2002-2004 period exhibited roughly parallel trends for the treated and control groups, which provides support for our research design. ", "The 2006-2008 utilization rates were generally lower for the treated groups than they were for the control groups. ", "The differences were especially pronounced for older age cohorts. ", "Our study suggests that the effects of disasters on health care utilization may persist for years after the event. ", "Recovery efforts may be improved by addressing both short-term and long-term health care interruptions. (", "Disaster Med Public Health Preparedness. ", "2019;13:724-731)." ]

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[ "Immediate versus conventional loading of palatal implants in humans: a first report of a multicenter RCT.", "\nThis study aims to analyze the clinical performance of two loading concepts on second-generation palatal implants (Orthosystem, Straumann, Basel, Switzerland) in a prospective multicenter randomized controlled clinical trial. ", "At the time of this interim analysis, 41 patients have been randomized on a 1:1 basis to one of two treatment groups. ", "Group 1 underwent conventional loading of palatal implants after a healing period of 12 weeks (gold standard) while group 2 underwent immediate implant loading within 1 week after implant insertion. ", "We report initial results at 6 months after functional loading. ", "The primary outcome parameter was implant success (no implant mobility, no implant loss). ", "The implants in both groups were initially stable at the time of insertion, and all were eligible for randomization. ", "Twenty-two patients (group 1) were subjected to conventional implant loading after 12 weeks while 19 patients (group 2) received immediate functional loading within the first week after insertion. ", "Direct (e.g. distal jet appliances) as well as indirect forms of anchorage (conventional or modified transpalatal arch) were used. ", "The magnitude of orthodontic forces ranged between 1 and 4 N for the immediate loading group and between 1 and 5 N for the conventional loading group. ", "One implant in group 1 was lost during the healing phase. ", "One dropout was registered in group 2. ", "Thirty-nine implants were functionally loaded for over 6 months now. ", "These preliminary data provide first evidence of the fact that immediate loading of palatal implants yields equivalent success rates as conventional loading to 4 N after 6 months." ]

{ "pile_set_name": "PubMed Abstracts" }

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[ "Hepatitis C virus infection and kidney transplantation: predictors of patient and graft survival.", "\nThe effect of hepatitis C virus (HCV) infection on patients undergoing kidney transplantation (KTx) is uncertain. ", "This study aimed to evaluate the outcomes of our HCV+/end-stage renal disease (ESRD) patient population based on the therapeutic option including KTx or continuation in dialysis. ", "KTx performed at Virginia Commonwealth University Hospital between January 2000 and December 2004 were tracked prospectively. ", "Forty-three out of a total of 394 KTx patients included in the analysis were HCV+. ", "A group of 52 contemporaneous HCV+/ESRD patients listed, but never transplanted, was also analyzed. ", "HCV-negative transplanted patients were used as the control group. ", "Patient survival posttransplantation was 81.4% and 68.5% at 1 and 3 years in the HCV+ group, and 97.1% and 92.9% at 1 and 3 years in the HCV- group, respectively (P=0.001). ", "Graft survival was 81.2% and 64.1% at 1 and 3 years in the HCV+ group, and 93.2% and 84.1% at 1 and 3 years posttransplantation in the HCV- group (P=0.01). ", "Univariate analysis identified Knodell score as a predictor of mortality in HCV+ patients (P=0.04). ", "Cox proportional hazards multivariate analysis identified deceased donor (P=0.02), previous kidney transplant (P=0.007), pretransplant diabetes (P=0.05), and Knodell Score (P=0.012) as predictors of patient mortality. ", "Patient survival was superior in HCV+ patients undergoing KTx versus remaining on dialysis. ", "Patients with ESRD/HCV+ benefit from KTx without achieving the excellent survival of HCV-/ESRD patients. ", "Liver biopsy is a useful tool to identify advanced liver disease at pretransplantation time." ]

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[ "Mücü\n\nMücü (also, Myudzhyu) is a village and municipality in the Ismailli Rayon of Azerbaijan. ", " It has a population of 229.", "\n\nReferences \n\nCategory:Populated places in Ismailli District" ]

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[ "Q:\n\nBlogger Notable Template - Post Pagination Fix or Replacement?", "\n\nThe Blogger \"Notable\" template's post pagination link on the bottom of the main page only shows a \"More Posts\" link. ", "It's missing a \"Previous Posts\". ", "It's also missing the traditional \"Home\" link. ", "The \"More Posts\" link correctly disappears on the last page of posts.", "\nI am looking to enable at least a \"Previous Posts\" link.", "\nThis appears to be intentional on the part of Google as the code includes this:\n<div class='blog-pager container' id='blog-pager'> <b:include cond='data:newerPageUrl' name='previousPageLink'/> <b:include cond='data:olderPageUrl' name='nextPageLink'/> <b:include cond='data:view.url !", "= data:blog.homepageUrl' name='homePageLink'/></div>\n\nBut in two locations each the code includes:\n<b:includable id='previousPageLink'><!-- Don't show --></b:includable>\n\n<b:includable id='homePageLink'><!-- Don't show --></b:includable>\n\nI attempted to fix this by first altering this line:\n<a expr:href='data:blog.homepageUrl'>Home</a>\n\nThe only thing that did was the \"Home\" link to appear on the last page of posts where the \"More Posts\" previous was placed. ", "Several other examples found online could not be tried as they refer to code that no longer exists within templates.", "\n\nI've also tried at least a dozen 3rd party numbered pagination coding schemes which overwrite Blogger's existing code, but those do not work correctly.", "\nAny idea of how to fix the template to enable the links or 3rd party code that might work?", "\n\nA:\n\nYou will need to replace -\n<b:includable id='previousPageLink'><!-- Don't show --></b:includable>\n\nwith \n<b:includable id='previousPageLink'>\n <a class='blog-pager-newer-link flat-button ripple' expr:href='data:newerPageUrl' expr:title='data:messages.newerPosts'>\n <data:messages.newerPosts/>\n </a>\n</b:includable>\n\nand replace\n<b:includable id='homePageLink'><!-- Don't show --></b:includable>\n\nwith\n<b:includable id='homePageLink'>\n <a class='home-link flat-button ripple' expr:href='data:blog.homepageUrl' expr:title='data:messages.home' >\n <data:messages.home/>\n </a>\n</b:includable>\n\nto show the Previous Posts (now called Newer Posts) and Home button in the page navigation. ", "Depending on theme being used, you will need to add custom CSS to make them appear correctly\n\n" ]

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[ "# frozen_string_literal: true\n# Be sure to restart your server when you modify this file.", "\n\n# You can add backtrace silencers for libraries that you're using but don't wish to see in your backtraces.", "\n# Rails.backtrace_cleaner.add_silencer { |line| line =~ /my_noisy_library/ }\n\n# You can also remove all the silencers if you're trying to debug a problem that might stem from framework code.", "\n# Rails.backtrace_cleaner.remove_silencers!", "\n" ]

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[ "Adenosine's effectiveness in long RP' re-entrant tachycardia: additional evidence of the decremental qualities of the retrograde limb.", "\nAdenosine's ability to terminate atrioventricular (AV) re-entrant supraventricular tachycardia is well documented. ", "Typically, termination occurs as a consequence of transient conduction block in the atrioventricular node, a tissue with decremental qualities. ", "However, the atrioventricular node is not always the site of action when adenosine is used on the re-entrant types of long RP' tachycardias. ", "These tachycardias are, in part, characterized by the decremental qualities of the retrograde limb of the tachycardia circuit, which, in turn, are typically exemplified by retrograde Wenckebach during ventricular (VVI) pacing during intracardiac electrophysiology studies. ", "This case report involves adenosine's ability to block conduction in the retrograde limb of the permanent form of junctional reciprocating tachycardia to provide further evidence as to the AV \"nodelike\" decremental qualities of this limb." ]

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[ "Regional (Dis)Unity in Southeast Asia\n\nJust weeks after Asian leaders waxed eloquent about unity at the 15th ASEAN Summit in Bangkok, a simmering diplomatic row between Southeast Asian neighbors Thailand and Cambodia threatens to boil over and tear efforts at regionalism asunder.", "\n\nThe dispute erupted when Cambodian Prime Minister Hun Sen decided to appoint fugitive former Thai premier and his longtime friend Thaksin Shinawatra as an economic adviser. ", "The move rankled Bangkok, which views the appointment of a convicted Thai citizen as interference in its internal affairs.", "\n\nBoth countries have since recalled their respective ambassadors, scrapped bilateral agreements on offshore resource exploration, triggered military alerts in border hotspots, and threatened to further downgrade relations. ", "Analysts say the relationship is at its lowest ebb since mid-2008, when the two countries exchanged deadly fire over the disputed Preah Vihear temple, killing more than a dozen troops.", "\n\nBut even if the cross-border saber-rattling continues, few expect it to descend into full-scale violence or all-out war. ", "The Cambodian leadership habitually stirs up international imbroglios to score domestic political points, and this case is likelyno different. ", "Mr. Hun Sen’s remarks on the sidelines of the ASEAN summit last month indicate that the ‘Thaksin gambit’ is merely retaliation for Bangkok allowing Cambodian opposition leader Sam Rainsy to deliver a searing rebuke of government policy at the Foreign Correspondent’s Club in September, rather than a deliberate attempt to vex Thailand. ", "With Thailand’s interior minister Chavarat Charnvirakul bearing the olive branch earlier this week and broaching the topic of talks, the bilateral spat is probably headed to the negotiating table instead of the battlefield.", "\n\nRobust economic relations will also likely inch along even if these prickly historical animosities do persist. ", "Thailandhasprovided tens of millions of dollars to Cambodia in grants and loans since the mid-1980s for infrastructure development. ", "And despite the barbs traded over ancient temples last year, bilateral trade surged from US$ 1.4 billion in 2007 to US$ 1.8 billion in 2008.", "\n\nThe regional implications of the squabble are more sobering. ", "The longer it continues, the more it will damage ASEAN’s credibility as a united organization behind the wheels of regional integration. ", "The timing is also particularly inopportune, as the group will look feckless and divided just as U.S. President Barack Obama visits the region later this week and both the Asia-Pacific Economic Cooperation (APEC) summit and the inaugural ASEAN-US Leaders Meeting are held this weekend. ", "ASEAN’s own Secretary General Surin Pitsuwanadmitsthat “ASEAN cannot afford to be seen as being so seriously divided”.", "\n\nBut unless the Thailand-Cambodia dispute is resolved over the next few days, the specter of mutual hostility will loom large even as Asian leaders air their trite encomiums on unity this weekend.", "\n\nAbout The Project 2049 Institute\n\nThe Project 2049 Institute seeks to guide decision makers toward a more secure Asia by the century’s mid-point. ", "The organization fills a gap in the public policy realm through forward-looking, region-specific research on alternative security and policy solutions, with an eye toward educating the public and informing policy debate." ]

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[ "Moral and ethical decisions: to be or not to be. ", "The 39th Walter J. Zeiter Lecture.", "\nThroughout history, some societies have short-changed the weak, the elderly, and children with disabilities. ", "In this lecture, I will explore some of the sad statistics related to dealing with people with disabilities, as well as attitudes toward, and treatments of, children and young adults with disabilities during the past 70 years. ", "I will follow this with some suggestions for change in our society's attitudes toward this vulnerable population." ]

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[ "EZ Yellow Revolution Cartridges\n\nThese are the latest EZ® Cartridge Tattoo Needles, the perfect choice for the tattoo artist giving an ultra-smooth feel with just the right amount of give.", "\nThe New Yellow Revolution Cartridges have the added safety of a membrane system." ]

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[ "Downtown Halifax Link\n\nThe Downtown Halifax Link system is similar to Toronto's PATH or Montreal's RÉSO system, but on a much smaller scale. ", "It consists of a network of climate-controlled pedways (pedestrian tunnels and skywalks) connecting various office buildings, hotels, parkades, and entertainment venues around downtown Halifax, Nova Scotia, Canada. ", "These walkways are all open to the public, and are convenient during inclement weather and the winter months.", "\n\nConnected buildings\nHotels:\nThe Prince George Hotel\nThe Hotel Halifax (formally Delta Halifax)\nThe Barrington Hotel (formally Delta Barrington)\nMarriott Halifax Harbourfront (formerly Casino Nova Scotia hotel)\n\nOffice buildings:\nTD Tower (Barrington Street)\nBarrington Tower (Scotia Square)\nDuke Tower (Scotia Square)\nCogswell Tower (Scotia Square)\nCIBC Building (Barrington Street)\nBrunswick Place formerly Trade Mart (Scotia Square)\nWorld Trade and Convention Centre\nPurdy's Wharf\nPurdy's Landing\nPurdy's Wharf Tower 1\nPurdy's Wharf Tower 2\n\nResidential:\nPlaza 1881 (Brunswick Street)\n\nEntertainment and retail:\nScotiabank Centre\nCasino Nova Scotia\nScotia Square Mall\nGranville Mall\nBarrington Place Shops\n\nProposed connections\nTrade Centre Limited (TCL), the developers of the new Halifax Convention Centre, have sought to connect the new facility with the Downtown Halifax Link via a new tunnel along Grafton Street. ", "Scott Ferguson, president of TCL, said that such a tunnel would help Halifax compete by linking the new centre with the existing network of hotel rooms. ", "The tunnel is expected to cost $7-10 million. ", "City staff are exploring possible alternatives but have not ruled the tunnel out.", "\n\nReferences\n\nExternal links\nDowntown Halifax Link website\n\nCategory:Buildings and structures in Halifax, Nova Scotia\nCategory:Pedways in Canada\nCategory:Skyways\nCategory:Underground cities" ]

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[ "Diskeeper Stylus Brush Review\n\nThe Diskeeper stylus brush is designed to keep your stylus clean and free of dirt and debris. ", "The brush features short densely packed fibers designed to properly remove dirt and gunk buildup, without damaging the stylus.", "\n\nMany people who own vinyl records practice decent maintenance and upkeep by cleaning the platter and their vinyl, but unfortunately, many people tend to overlook cleaning the stylus. ", "And often, newbies are afraid to clean the stylus simply because they’re so delicate and tend to bend easily. ", "But cleaning this component is actually crucial to sound quality and the integrity of your records.", "\n\nJust listening to your records can create natural wear and tear, especially to the stylus. ", "The small needle that extends from the cartridge and drags across the record to produce sound is called the stylus. ", "This tiny needle is very delicate and can accumulate dust buildup surprisingly fast.", "\n\nThe stylus also puts an impressive amount of pressure per inch on a record, which is why it’s crucial that it’s properly maintained.", "\n\nThere are many common cleaning methods out there that you can try when it comes to keeping your stylus clean, but using a stylus brush, such as this model by Sleeve City, is an easy, fast, and efficient way to ensure that you enjoy the best sound possible.", "\n\nStylus Brush Overview and Features\n\nA dirty stylus can totally ruin your listening experience. ", "So, if your vinyl doesn’t sound quite as good as it used to, the first thing you should check out is the stylus.", "\n\nIdeally, you should use the Diskeeper and clean the stylus frequently, depending on how often you use your turntable. ", "Some audiophiles recommend cleaning it once a week if you listen to records daily.", "\n\nWhile there are many stylus cleaning kits on the market, we’ve found that the simplest methods are usually the best and the most effective. ", "Using the stylus brush you can gently remove dirt and debris build-up without worrying about harmful chemicals penetrating the cartridge. ", "Brush cleaning the stylus is also probably one of the most popular DIY cleaning methods available and it’s a more affordable option than purchasing an expensive cleaning kit.", "\n\nMany experts believe that keeping the stylus free of debris is the key to getting the best listening experience out of your vinyl, not to mention preserving them. ", "This stylus brush is designed to handle heavy use and works to make cleaning your stylus a fast and efficient process. ", "Once it’s been cleaned, you’ll notice less distortion, surface noise, and popping. ", "We recommend always brushing from the back of the stylus, which is the end that’s nearest to the cantilever, and toward the tip. ", "You never want to brush the stylus from side to side or from the front to the back. ", "Doing so can damage and even bend the needle.", "\n\nPreserving the Life of Your Stylus\n\n• To thoroughly clean the needle, use the brush with distilled water, brushing from back to front. ", "If you prefer to use a commercial cleaning product, be very careful which product you choose because the wrong one can damage the stylus.", "\n\n• When cleaning the stylus, make sure you regulate the changer mechanism or the tonearm set-down in order to prevent the needle from striking the edge of the vinyl or record player.", "\n\n• Never handle the tonearm when a record is playing. ", "Doing so can cause the arm to sweep across the vinyl and scratch it.", "\n\n• If a manual set-down is a must, make sure you release the tonearm as soon as the needle engages the groove.", "\n\n• Never activate the tonearm without a record on the platter.", "\n\n• Never play a severely damaged record.", "\n\n• Before use, make sure that the cartridge is mounted to the tonearm correctly.", "\n\n• For each type of cartridge and stylus make sure you’re using the appropriate vertical tracking force. ", "Using a force that’s outside the recommended range can damage the stylus.", "\n\nDiskeeper Pros and Cons\n\nPros: This brush is a great buy for the audiophile on a budget. ", "In our opinion, the brush not only works better than expensive cleaning kits, but it’s also much easier and easier to use. ", "The brush allows you to clean the stylus by removing visible gunk and dust buildup.", "\n\nThe bristle design is perfect for picking up even the smallest dust particles. ", "The close bristle design ensures that it makes close contact with the entire surface of the stylus. ", "Some consumers recommend dry brushing for the best results, while others felt that wetting the brush and dipping it into a liquid dish soap and water mixture worked better. ", "We don’t recommend a wet cleaning technique simply because you’ll risk damaging the internal components of the cartridge.", "\n\nCons: While the brush works great, we wish it was a little larger. ", "This incredibly small brush can be hard to hang onto if you have large hands. ", "The size of the brush was probably the biggest complaint among consumers, however, most stylus brushes are around the same size. ", "A slightly longer and wider handle would definitely solve this issue; however, the size of the brush and handle can actually allow you to access and clean the stylus more efficiently, compared to a brush with a bulkier design.", "\n\nStylus Brush by Diskeeper Conclusion and Rating\n\nThis innovative Diskeeper stylus brush is a handy tool to have around, especially if you play your records on a daily basis. ", "The bristle design ensures that the needle is thoroughly cleaned after use, which can help to prevent poor sound quality and needle and vinyl damage. ", "While routine maintenance is often overlooked by many vinyl lovers, consistently cleaning the stylus is a must if you want to preserve the quality of the needle and improve your listening experience. ", "We gave this stylus a rating of four and a half out of five stars and felt it was one of the best models on the market, easily beating out higher priced stylus brushes, due to overall quality and durability.", "\n\nRelated Posts:\n\nThe 5 Best Portable Record Players Of 2018 We have rounded up the best portable record players (a.k.a turntables). ", "Our review focuses on sound quality, usability and features like speakers, bluetooth, USB, etc., ", "to help you find the best turntable online. ", "After all vinyl is back, BOOM!…", "\n\nHow To Clean A Record Stylus And Lengthen Your… When you listen to a record, you may notice a lot of hisses and pops, but it doesn’t have to be that way. ", "In reality, this type of surface noise is usually preventable. ", "The first step is to ensure…\n\nCollector Protector Vinyl Cleaner And Carbon Fiber… The Collector Protector record spray and carbon fiber record brush set are designed to keep your vinyl sounding its best. ", "This package comes with a bottle of cleaning solution and a brush made from carbon fiber, which won’t scratch…\n\nSearch\n\nHi I’m Jon\n\nHey there beautiful people…\n\nThis is Jon here. ", "First, before anything else, let me just come clean. ", "I’m totally nuts about music to the point of obsession. ", "There I said it and now I can tell more about this blog with a clear conscience ha ha ha.", "\n\nI’m not done there’s more, check out my About page so I can feel important!", "\n\nBuyer’s Guide\n\nDisclosure\n\nwww.portablemusicnerd.com is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to (www.portablemusicnerd.com) (amazon.com, or endless.com, MYHABIT.com, SmallParts.com, or AmazonWireless.com)" ]

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[ "Australia seems to be becoming a more polarised society. ", "This is the simple conclusion from recent research undertaken for SBS, which looked for answers to how Australians think the country has changed over the past 20 years, and where they think it may be in another 20 years.", "\n\nA more “traditionalist” group (perhaps as high as 47%) wants conservative certainties, rejecting or fearing social change. ", "A large middle group (around a third of Australians) is “open-minded” about the future, but highly protective of its own lifestyles and interests. ", "Only a “cosmopolitan” minority (one in five) is drawn towards new opportunities while welcoming an evolving and changing world.", "\n\nEvidence from the Census for the past two decades reveals some basic information. ", "Australians are ageing; we are more culturally diverse; we live in smaller family units or alone; we are less religious; and we consume more stuff per head.", "\n\nThe divisions between us – the shape of the society we desire and the threats we fear – are deepening. ", "The focus is on apprehension about, as against desire for, diversity and innovation. ", "The multicultural future that all expect to increase lies at the heart of these tensions.", "\n\nThose surveyed agree that the main changes that have happened are those that have made us more multicultural and more materialistic. ", "Over half of those asked believe that 20 years ago, Australians were easygoing, friendly and outgoing, trustworthy, unpretentious and “tough”. ", "But today, less than half believe that these descriptions are accurate.", "\n\nWe do think, though, that we’ve become more social – moving out from a concentration on family – and slightly more open-minded, intelligent and creative, though hugely more materialistic. ", "We are as racist and discriminatory, and a bit less sexist – though much more ageist – than we were then.", "\n\nMateship, though, is on the decline; we whinge more; and we’re less positive and optimistic. ", "There is a huge gap between between “how Australians see themselves in the media” and “how Australians really are”.", "\n\nThe next generation, we believe, will continue to experience a multicultural society, though we are very divided on what we think of this. ", "Our concerns are affected by how we think we will be placed in the future economy. ", "While a significant group see an improved quality of life (37%), almost as significant a group see the future as leaving them worse off (28%).", "\n\nThe positive shape of the future has to do almost totally with economic opportunity. ", "The negative aspects are both economic and social, with competition for employment and a perception of too many immigrants contributing to the apprehension.", "\n\nGiven the unanimity about our continuing development as an immigration society, Australians’ worries bear out similar work by Monash University for the Scanlon Foundation. ", "The SBS-commissioned research reveals two clusters of values at work: immigrants are threatening when they “don’t buy into the Australian way of life”, “don’t speak English” and “contribute to overpopulation”.", "\n\nOthers, however, take an opposite view: they worry about racism in Australia, Australia’s harsh policies on asylum seekers and our perceived lack of tolerance.", "\n\nOf those surveyed, Australians of non-Anglo background are far more likely to agree that Australia is much less racist than it used to be, while “Anglos” think we have stayed much the same. ", "Non-Anglos see less materialism in Australia than Anglo-Australians. ", "They are more trusting of immigrants, while being more fearful of the expansion of racism in the future.", "\n\nSo what does research like this do for an organisation like SBS, which strives to reflect Australian multiculturalism? ", "The fact that Australia is becoming more diverse suggests the future looks good. ", "But with potentially half the sample being “traditionalists” who are looking for confirmation of their prejudices, there is still a hefty base for the Anglo-conformity of the mainstream commercial channels and the ABC.", "\n\nIn a sense, then, SBS has a three-pronged challenge. ", "Firstly, it has to treat the cosmopolitans with respect, hold them, and feed their hunger for innovation, diversity and exploration. ", "Secondly, it has to convince the open-minded that the experience it offers is exciting enough without being scary – that it’s not just about “Sex Before Soccer” (though the soccer is what will position the channel in this, a World Cup year).", "\n\nThen there’s the traditionalists. ", "Does SBS try to win some of them over (they are the heartland of the big-money spenders on advertising staples), or give them away because chasing them could too easily compromise the brand for the 53% who are already potentially onside?", "\n\nThe research seems to be saying we need and many people want social institutions, including broadcasters and social media sites, that will respect diversity, celebrate creativity and build integration between different communities and generations. ", "There’s already research that shows how social media like Facebook are weaving together new networks of friendship that until then were dissipating in the rush to individualism and materialist self-indulgence.", "\n\nNew communities of interest and association are forming, and not dissolving again as used to be the case in the earlier years of the internet. ", "Now they are clumping people together for longer, allowing networks to spread.", "\n\nThe research suggests that SBS would be well advised to further build its own unique brand. ", "It can become an institution that knits together Australia’s diversity as an immigration nation." ]

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[ "Miracle Plants That Melt Belly Fat\n\nAlthough there is no magic formula to lose weight, besides a healthy lifestyle, you can try some natural remedies that will help you to get rid of the belly fat. ", "These natural remedies are: diuretic and laxative teas, foods that cut your appetite or healing herbs that stimulate your metabolism.", "\n\nThere are two categories of plants that help you to obtain the desired silhouette: purifying plants used in releasing of liquids retained in the body and plants that stimulate the metabolism.", "\n\nAloe leaves against belly fat\n\nAloe leaves are situated in the top of plants used to lose weight. ", "This plant helps detoxify, accelerates fat burning and regulate bowel movements. ", "Has many effects that help you to lose weight like: laxative and diuretic strong effects. ", "In addition, aloe leaves inhibit appetite, especially systemic administration over longer periods of time.", "\n\nElderflower against belly fat\n\nDue to active elements from its composition elderflower a great remedy against belly fat. ", "As a tea, tincture or juice has a diaphoretic and diuretic action that helps to eliminate the water from the body. ", "It is also a plant that reduces appetite and has a laxative effect. ", "Attention: consumed in large quantities, can give side effects.", "\n\nCelery leaves against belly fat\n\nVery rich in water and fiber, celery leaves are perfect if you want to accelerate fat burning and to lose weight very fast. ", "If you eat frequently celery leaves( or drink juice made with celery leaves), they will reduce blood pressure and stimulate bowel cleansing.", "\n\nGreen tea against belly fat\n\nGreen tea helps to speed up metabolism and this in why is recommended in slimming diets. ", "Is a good drink, without calories and beneficial to get rid of extra pounds. ", "Fights against water retention in the body, stimulates digestion, combats constipation, detoxifies the body and has an energizing effect.", "\n\nNettle against belly fat\n\nNettle is a source of vitamins (A, B, C, E, K), and minerals (iron, calcium, magnesium, phosphorus, potassium) which are beneficial to the body. ", "In the same time, contains substances that suppress appetite, which makes it ideal in a diet. ", "It also has a low glycemic index and provides energy." ]

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[ "// Copyright 2015 The Go Authors. ", "All rights reserved.", "\n// Use of this source code is governed by a BSD-style\n// license that can be found in the LICENSE file.", "\n\npackage pkcs12\n\nimport (\n\t\"bytes\"\n\t\"crypto/cipher\"\n\t\"crypto/des\"\n\t\"crypto/x509/pkix\"\n\t\"encoding/asn1\"\n\t\"errors\"\n\n\t\"golang.org/x/crypto/pkcs12/internal/rc2\"\n)\n\nvar (\n\toidPBEWithSHAAnd3KeyTripleDESCBC = asn1.ObjectIdentifier([]int{1, 2, 840, 113549, 1, 12, 1, 3})\n\toidPBEWithSHAAnd40BitRC2CBC = asn1.ObjectIdentifier([]int{1, 2, 840, 113549, 1, 12, 1, 6})\n)\n\n// pbeCipher is an abstraction of a PKCS#12 cipher.", "\ntype pbeCipher interface {\n\t// create returns a cipher.", "Block given a key.", "\n\tcreate(key []byte) (cipher.", "Block, error)\n\t// deriveKey returns a key derived from the given password and salt.", "\n\tderiveKey(salt, password []byte, iterations int) []byte\n\t// deriveKey returns an IV derived from the given password and salt.", "\n\tderiveIV(salt, password []byte, iterations int) []byte\n}\n\ntype shaWithTripleDESCBC struct{}\n\nfunc (shaWithTripleDESCBC) create(key []byte) (cipher.", "Block, error) {\n\treturn des.", "NewTripleDESCipher(key)\n}\n\nfunc (shaWithTripleDESCBC) deriveKey(salt, password []byte, iterations int) []byte {\n\treturn pbkdf(sha1Sum, 20, 64, salt, password, iterations, 1, 24)\n}\n\nfunc (shaWithTripleDESCBC) deriveIV(salt, password []byte, iterations int) []byte {\n\treturn pbkdf(sha1Sum, 20, 64, salt, password, iterations, 2, 8)\n}\n\ntype shaWith40BitRC2CBC struct{}\n\nfunc (shaWith40BitRC2CBC) create(key []byte) (cipher.", "Block, error) {\n\treturn rc2.New(key, len(key)*8)\n}\n\nfunc (shaWith40BitRC2CBC) deriveKey(salt, password []byte, iterations int) []byte {\n\treturn pbkdf(sha1Sum, 20, 64, salt, password, iterations, 1, 5)\n}\n\nfunc (shaWith40BitRC2CBC) deriveIV(salt, password []byte, iterations int) []byte {\n\treturn pbkdf(sha1Sum, 20, 64, salt, password, iterations, 2, 8)\n}\n\ntype pbeParams struct {\n\tSalt []byte\n\tIterations int\n}\n\nfunc pbDecrypterFor(algorithm pkix.", "AlgorithmIdentifier, password []byte) (cipher.", "BlockMode, int, error) {\n\tvar cipherType pbeCipher\n\n\tswitch {\n\tcase algorithm.", "Algorithm.", "Equal(oidPBEWithSHAAnd3KeyTripleDESCBC):\n\t\tcipherType = shaWithTripleDESCBC{}\n\tcase algorithm.", "Algorithm.", "Equal(oidPBEWithSHAAnd40BitRC2CBC):\n\t\tcipherType = shaWith40BitRC2CBC{}\n\tdefault:\n\t\treturn nil, 0, NotImplementedError(\"algorithm \" + algorithm.", "Algorithm.", "String() + \" is not supported\")\n\t}\n\n\tvar params pbeParams\n\tif err := unmarshal(algorithm.", "Parameters.", "FullBytes, &params); err !", "= nil {\n\t\treturn nil, 0, err\n\t}\n\n\tkey := cipherType.deriveKey(params.", "Salt, password, params.", "Iterations)\n\tiv := cipherType.deriveIV(params.", "Salt, password, params.", "Iterations)\n\n\tblock, err := cipherType.create(key)\n\tif err !", "= nil {\n\t\treturn nil, 0, err\n\t}\n\n\treturn cipher.", "NewCBCDecrypter(block, iv), block.", "BlockSize(), nil\n}\n\nfunc pbDecrypt(info decryptable, password []byte) (decrypted []byte, err error) {\n\tcbc, blockSize, err := pbDecrypterFor(info.", "Algorithm(), password)\n\tif err !", "= nil {\n\t\treturn nil, err\n\t}\n\n\tencrypted := info.", "Data()\n\tif len(encrypted) == 0 {\n\t\treturn nil, errors.", "New(\"pkcs12: empty encrypted data\")\n\t}\n\tif len(encrypted)%blockSize !", "= 0 {\n\t\treturn nil, errors.", "New(\"pkcs12: input is not a multiple of the block size\")\n\t}\n\tdecrypted = make([]byte, len(encrypted))\n\tcbc.", "CryptBlocks(decrypted, encrypted)\n\n\tpsLen := int(decrypted[len(decrypted)-1])\n\tif psLen == 0 || psLen > blockSize {\n\t\treturn nil, ErrDecryption\n\t}\n\n\tif len(decrypted) < psLen {\n\t\treturn nil, ErrDecryption\n\t}\n\tps := decrypted[len(decrypted)-psLen:]\n\tdecrypted = decrypted[:len(decrypted)-psLen]\n\tif bytes.", "Compare(ps, bytes.", "Repeat([]byte{byte(psLen)}, psLen)) !", "= 0 {\n\t\treturn nil, ErrDecryption\n\t}\n\n\treturn\n}\n\n// decryptable abstracts an object that contains ciphertext.", "\ntype decryptable interface {\n\tAlgorithm() pkix.", "AlgorithmIdentifier\n\tData() []byte\n}\n" ]

{ "pile_set_name": "Github" }

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[ "PHILIPSFW-C100/37 Owner's Manual\n\nTweet about this product and get $1.00 of store credit for instant use!", "\n\nDownload\n\nPDF Format\n\nComplete manual\n\nLanguage: English\n\nPrice: $4.99\n\nDescription of PHILIPS FW-C100/37 Owner's Manual\n\nComplete owner's manual in digital format. ", "The manual will be available for download as PDF file after You purchase it.", "\n\nOwner's Manual ( sometimes referred to as User's Guide or User's Manual ) contains information on how to use Your device. ", "After placing order we'll send You download instructions on Your email address.", "\n\nThe manual was complete and of great quality. ", "Originally a tri-lingual file, I first received only one language. ", "After a note to owners-manuals.com, I quickly received the remaining languages... Great service, definitely worth it.", "\n\nThank you for providing this manual and at low cost.", "\nThe Philips scope is of excellent quality, longevity and build and had a couple of faults\nwhen it was passed to me. ", "Having the CCT diagrams is a blessing.", "\nI have fixed the problems and also modded the scope to my requirements.", "\nI have built a 24v Li-Ion pack for portable use from old but good laptop batts.", "\nit is working beautifully and I am well pleased. ", "Keep up the good work Guys.", "\n\nAwesome quality manual. ", "You really saved my bacon with this one. ", "Was looking for some specific information with regards to my \"new\" vintage VCR that didn't come with the owners manual. ", "This site is truely a goldmine of available manuals. ", "The quality of the scans are top notch.", "\nThank-you so much for this awesome manual. ", "If you're looking for this Sony SL-HF400 owners manual, this is the one you NEED to buy. ", "Definitely worth the money.", "\n\nThe manual was made available promptly. ", "I is a clean scan of the original. ", "I had no problem downloading it. ", "The scan was well centered and cleanly formatted. ", "It is as good a product as can be had without being the original document.", "\n\nLoad a blank tape into tape deck 1 and a disc into the disc tray. ", "2 Press CD. ", "¶ You can program the tracks in the order you want them to be recorded (see Programming Tracks). ", "If you do not, the tracks are recorded according to the order on the selected disc. ", "3 Press RECORD on tape deck 1 to start recording. ", "➜ The REC starts flashing. ", "4 Press STOP•OPEN on tape deck 1 to stop recording, then press Ç to stop CD playback.", "\n\nNotes: – At the end of side A, flip the tapes to side B and repeat the procedure. ", "– Dubbing of tapes is only possible from tape deck 2 to tape deck 1. ", "– To ensure good dubbing, use tapes of the same length." ]

{ "pile_set_name": "Pile-CC" }

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[ "Nowadays, various mobile communication systems are put to practical use along with the advancement of radio communication technologies. ", "For example, mobile communication systems compliant with schemes such as PDC, CDMA and PHS are put to practical use in Japan.", "\nAlong with the practical use of various mobile communication systems, multiband radio communication devices (such as cellular phone terminals) supporting multiple frequency bands (multiband) have been provided. ", "Specifically, a multiband radio communication device is capable of transmitting and receiving simultaneously multiple radio signals in different frequency bands.", "\nIn a multiband radio communication device, in order to prevent a radio signal in a certain frequency band from entering, as noise, into a receiver circuit for receiving a radio signal in a different frequency band, a filter that suppresses the noise is provided in general (refer to Japanese Patent Application Publication No. ", "Hei 11-112382 (pages 4 to 5 and FIG. ", "1) for example)." ]

{ "pile_set_name": "USPTO Backgrounds" }

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[ "Early pregnancy diagnosis in the sow by saliva progesterone measurement using a bovine milk progesterone qualitative test EIA kit.", "\nWe attempted to measure the qualitative saliva progesterone concentration in the sow using a commercial bovine milk progesterone qualitative test EIA kit (qualitative kit), which can measure the progesterone concentration in approximately 10 min, and investigated the possibility of applying this method of progesterone concentration measurement to early pregnancy diagnosis in the sow. ", "The accuracy of pregnancy diagnosis at 17-24 days after last mating for 138 sows was 91.3% (105/115) for positive cases and 100% (6/6) for negative cases. ", "The overall pregnancy diagnosis accuracy, including 17 indeterminable cases, was 80.4% (111/138). ", "A comparison of the diagnoses based on progesterone concentrations measured by the qualitative kit and the saliva progesterone concentrations of identical samples measured by the quantitative kit showed close agreement: 6 cases diagnosed as negative pregnancy by the qualitative kit all had a progesterone concentration of less than 5 ng/ml, while 111 out of 115 cases diagnosed as positive pregnancy by the qualitative kit all showed a progesterone concentration over 5 ng/ml. ", "Thus, the results of this study show that qualitative measurement of the saliva progesterone concentration in the sow using a bovine milk progesterone qualitative test EIA kit is a practical method for early pregnancy diagnosis." ]

{ "pile_set_name": "PubMed Abstracts" }

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[ "Carers WA, Consumers of Mental Health WA and Helping Minds (formerly Arafmi) are establishing a peer-led network of consumers and carers accessing WA NDIS My Way in Cockburn-Kwinana. ", "People with psychosocial disability (due to mental health issues), their families and carers are welcome at this first network meeting.", "\n\nAre you potentially eligible for, or already participating in, the WA NDIS My Way trial in the Cockburn-Kwinana area? ", "Come to our expo and find out more about the variety of therapy supports and services you may be able to access." ]

{ "pile_set_name": "Pile-CC" }

[ 0.01092896174863388, 0, 0, 0 ]

[ "Belfast Health and Social Care Trust; South Eastern Health and Social Care Trust, Belfast; : St. Mary’s Hospital, Manchester\n\nPrincipal Investigator:\n\nV.Holmes\n\nOther Investigators:\n\nF.Alderdice; D.McCance; R.Harper; C.Patterson; M.Maresh\n\nLocations of the project:\n\nBelfast and Manchester (United Kingdom)\n\nAmount allocated:\n\nUSD 359,406\n\nDate:\n\nOctober 1, 2011 - April 30, 2015\n\nObjectives:\n\nThis project will evaluate, in a multi-centre randomized controlled trial, the effect of an educational DVD on anxiety, stress, emotional adjustment, glycaemic control and knowledge in women diagnosed with gestational diabetes mellitus (GDM). ", "The DVD will combine the views and experiences of women with GDM alongside an evidence-based commentary, to increase the knowledge and skills required to manage GDM, leading to a sense of empowerment and allowing women to regain control of their lives. ", "As women with GDM have a higher risk of developing type 2 diabetes, this DVD will harness a unique opportunity to intervene in the progression to diabetes.", "\n\nBRIDGES (Bringing Research in Diabetes to Global Environments and Systems) is a programme initiated by the International Diabetes Federation[3], and supported by an educational grant from Lilly Diabetes." ]

{ "pile_set_name": "Pile-CC" }

[ 0.015698587127158554, 0.007905138339920948, 0.0064516129032258064, 0.01951219512195122 ]

[ "1. ", "Field of the Invention\nThe present invention relates to an arrangement for imposing pressure on cleaning media and/or lubricants which are contained as maintenance media in the movable components of medical, particularly dental handpieces, wherein the maintenance medium is adapted to be placed under pressure by a pressure drive acting through an outlet opening of a housing which contains a motion drive for the movable handpiece components, the last mentioned being brought into connection with the outlet opening through an inlet opening in the handpiece. ", "During this pressurization of the maintenance medium, the movable components of the handpiece are placeable into movement through the motion drive of the housing in such a manner, whereby engaging means of the motion drive which are accessible through the outlet opening of the housing can be brought into engagement with cooperating engaging means of the movable components of the handpiece which are accessible through the inlet opening.", "\nThe maintenance medium can be constituted of a liquid cleaning medium and/or lubricant, for example oil, if required admixed with a solvent and/or a preferably gaseous drive medium. ", "For example, there can be employed a maintenance medium pursuant to German Laid-open patent application No. ", "29 16 552. ", "After the passage of the maintenance medium through the handpiece, through the intermediary of the pressure drive or, in essence, by means of the drive medium or through compressed air, there is carried out a drying of the handpiece so that, for instance, the solvent medium will evaporate and be blown out by the pressure drive from the handpiece while the oil components remain within the handpiece. ", "The motion drive prior thereto hereby effects or intensifies an effective moistening with maintenance medium of the movable handpiece components.", "\n2. ", "Discussion of the Prior Art\nAn arrangement of the above mentioned type has become known from the brochure \"Turboclean\" issued by the firm Scania Dental AB. ", "In this known arrangement, only handpieces of one and the same handpiece type, in essence, with completely identical cooperating engaging means correlated with the engaging means of the motion drive, can always be attached on the outlet opening of the housing and and maintained in the described manner. ", "Handpieces or handpiece components which include different cooperating engaging means, in particular attachment heads which are attachable on the handpiece gripping sleeve, the attachment heads in a condition separated from the handpiece gripping sleeve, accordingly cannot be attached on the outlet opening of the housing while maintaining movement of their movable components. ", "In the attached condition, the attachment heads or their movable components, are only inadequately or not at all supplied with the maintenance medium, since the maintenance medium which is introduced into the handpiece at the end remote from the work tool, as viewed in its flow direction, will already deposit itself in the handpiece gripping sleeve or the movable portions thereof ahead of the attachment head, and is already used up prior to reaching the attachment head." ]

{ "pile_set_name": "USPTO Backgrounds" }

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[ "Synergistic inhibition of the calcification of glutaraldehyde pretreated bovine pericardium in a rat subdermal model by FeCl3 and ethanehydroxydiphosphonate: preincubation and polymeric controlled release studies.", "\nCalcification is a frequent cause of the clinical failure of bioprosthetic heart valves fabricated from glutaraldehyde-pretreated porcine aortic valves or glutaraldehyde-pretreated bovine pericardium (GPBP). ", "We investigated the hypothesis that ferric chloride (FeCl3) and sodium-ethanehydroxydiphosphonate (EHDP) may act synergistically to prevent bioprosthetic tissue calcification. ", "Pre-incubations and controlled release systems were studied individually. ", "FeCl3-EHDP polymeric controlled release matrices were formulated using silicone rubber and evaluated for in vitro release kinetics at pH 7.4 and 37 degrees C. The effects of Fe-EHDP synergism on GPBP calcification were investigated with 21 d subdermal implants in 3 wk-old male rats. ", "Results demonstrated that levels of Fe3+ and EHDP uptake, measured in GPBP tissues pre-incubated first in an FeCl3 solution (10(-5) M) followed by an EHDP solution (0.1 M), were higher than in the reverse order of incubation. ", "In the first series of rat implants, GPBP was pre-incubated in either FeCl3 or Na2EHDP solutions, or sequential pre-incubations of first FeCl3 and then Na2EHDP solutions, or the reverse. ", "The inhibition of calcification was greatest when FeCl3 (first pre-incubation, 10(-5) M) was combined with Na2EHDP (second pre-incubation, 0.1 M) (1.78 +/- 0.2 micrograms of Ca2+/mg of dried tissue) compared with the other pre-incubation groups: EHDP (first pre-incubation) combined with FeCl3 (second pre-incubation) (21.7 +/- 6.4), FeCl3 solution alone at 10(-5) M (27.9 +/- 10.7), Na2EHDP solution alone at 0.1 M (52.3 +/- 11.9) and the control group (72.3 +/- 10.2). ", "In a second series of implants, GPBP specimens were co-implanted with individual controlled release systems containing one of the following formulations (weight percentage in silicone rubber): 1% FeCl3, 20% CaEHDP, 20% protamine sulphate, 1% FeCl3-20% CaEHDP, and 1% FeCl3-20% protamine sulphate. ", "The 1% FeCl3-20% CaEHDP silicone-rubber matrices were the most effective for inhibiting GPBP mineralization (13.7 +/- 3.0 micrograms Ca2+/mg of dried tissue) compared with non-drug silicone co-implant controls (74.7 +/- 5.58 micrograms Ca2+/mg of dried tissue) and other polymeric treatment groups (32.3 +/- 2.3-80.0 +/- 19.7). ", "No adverse effects on bone or overall growth of any treatment protocols were noted. ", "Thus, combinations of FeCl3 and EHDP, using either pre-incubations or polymeric controlled release, were synergistic for inhibiting GPBP calcification." ]

{ "pile_set_name": "PubMed Abstracts" }

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[ "Systemic aspects of interstitial cystitis, immunology and linkage with autoimmune disorders.", "\nIt is recognized that interstitial cystitis (IC) is often associated with a number of diseases such as allergies, irritable bowel syndrome, fibromyalgia, inflammatory bowel disease (Crohn's disease and ulcerative colitis), systemic lupus erythematosus, and Sjögren's syndrome. ", "The prevalence of allergies in IC is reported to be between 40 and 80% of patients. ", "The background of the association is not known and does not seem to be the result of a generalized allergic constitution. ", "Some report that treatment of allergy sometimes has a beneficial effect on bladder symptoms. ", "An increased expression of certain growth factors (PD-ECGF, FGF, and VEGF) has been found in the bladder of IC patients. ", "In addition, the expression of CD44 was significantly higher in ulcer type IC than in non-ulcer type. ", "In general, these growth factors are soluble and diffusible under normal conditions but proteoglycans such as CD44 could bind to these growth factors. ", "This may promote the accumulation of growth factors at the sites of inflammation. ", "CD44 expression in ulcer type IC could explain the prolonged and stronger expression of GAG-binding growth factors that promote inflammation. ", "In the Rotterdam study, a strong association between IC and Sjögren's syndrome is recognized. ", "In this study, 28% of IC patients have definite or probable Sjögren's syndrome. ", "This association is much stronger than is generally recognized. ", "This could be due to difficulties in diagnosing Sjögren's syndrome since a diagnosis usually requires a high index of suspicion." ]

{ "pile_set_name": "PubMed Abstracts" }

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[ "Highest quality care.", "\n\nRight here at home.", "\n\nICU/Telemetry\n\nWhen your loved one is in the Intensive Care Unit (ICU) at Morehouse General Hospital, the staff understands how overwhelming and stressful it can be. ", "Sometimes a patient’s stay in the ICU is planned; sometimes it is quite unexpected. ", "Whatever condition or event, ICU patients all require intensive treatment, monitoring and support that is only available in an ICU setting.", "\n\nMorehouse General also understands how much you want to be there for your loved one. ", "You are an important member of the ICU team and can help in your loved one’s recovery just by visiting them. ", "Sometimes, visiting a loved one who is critically ill is not easy. ", "Members of the ICU staff recognize your contribution to the team and the importance of your visits to the patient’s well-being. ", "Visiting hours play an integral role in an ICU for both patients and health care providers.", "\n\nICU visitation hours are as follows:\n\n8:00 – 8:15am\n\n12:00 – 12:15pm\n\n5:00 – 5:15pm\n\n8:00 – 8:15pm\n\nEach patient is allowed visitors, but they must be over the age of 12. ", "This will enable your loved one to obtain adequate rest and help with their recovery time. ", "The set times will also allow the staff to ensure your loved one is “always very satisfied” with their care and that their need for rest and privacy is respected." ]

{ "pile_set_name": "Pile-CC" }

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[ "George Vincent McLaughlin\n\nGeorge Vincent McLaughlin (May 20, 1887 – December 7, 1967) was superintendent of the New York State Banking Department in 1920. ", "He was the New York City Police Commissioner from 1926 to 1927 and president of the Brooklyn Trust Company in 1940; and vice chairman of the Triborough Bridge and Tunnel Authority. ", "McLaughlin was of Irish American heritage.", "\n\nBiography\nHe was born on May 20, 1887. ", "He served as the New York City Police Commissioner from January 1, 1926 to April 12, 1927.", "\n\nTime magazine wrote on August 23, 1926:\nLast week Detective John Singer of Manhattan arrested a buck Negro for stealing a car, bought him some sandwiches and coffee, took him to Police Headquarters. ", "It was hot. ", "Officer Singer removed his coat, sat down to fill out the prisoner's pedigree card. ", "Suddenly Negro Pierce snatched a revolver from Officer Singer's hip pocket, shot him three times to the death, escaped. ", "One Kuku, a witness, was the only other person in the room. ", "Later Murderer Pierce was captured in the Bowery after a taxicab chase. ", "He told the police: \"I shot the detective; I'm sorry.\" ", "Manhattanites were shocked. ", "John Singer was the sixth police-man to be killed on duty since January 1, 1926; eleven others had been shot, merely wounded. ", "Police Commissioner George V. McLaughlin emitted a soothing statement: \"We are getting all the bad breaks so far. ", "The police are making splendid arrests, but the luck is against them.\"", "\n\nGeorge, as president of the Brooklyn Trust Company brought Walter O'Malley into the financial arrangements for Ebbets Field in 1940. ", "In 1947 he was awarded an honorary degree from Fordham University. ", "He was a delegate to the 1952 Democratic National Convention for the 17th District. ", "McLaughlin was a member of Robert Moses's Triborough Bridge and Tunnel Authority.", "\n\nHe died on December 7, 1967.", "\n\nReferences\n\nCategory:1887 births\nCategory:1967 deaths\nCategory:New York City Police Commissioners\nCategory:American people of Irish descent" ]

{ "pile_set_name": "Wikipedia (en)" }

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[ "name = Boston Content Type Person Profile\ndescription = Boston Content Type Person Profile\ncore = 7.x\npackage = Boston\nversion = 7.x-1.0\nproject = bos_content_type_person_profile\ndependencies[] = addressfield\ndependencies[] = bos_shared_fields\ndependencies[] = bos_vocabulary_political_party\ndependencies[] = bos_vocabulary_profile_type\ndependencies[] = ctools\ndependencies[] = entityreference\ndependencies[] = features\ndependencies[] = field_group\ndependencies[] = image\ndependencies[] = list\ndependencies[] = media\ndependencies[] = options\ndependencies[] = paragraphs\ndependencies[] = strongarm\ndependencies[] = text\nfeatures[ctools][] = field_group:field_group:1\nfeatures[ctools][] = strongarm:strongarm:1\nfeatures[features_api][] = api:2\nfeatures[field_group][] = group_components|node|person_profile|form\nfeatures[field_group][] = group_person_biography|node|person_profile|form\nfeatures[field_group][] = group_person_contact_info|node|person_profile|form\nfeatures[field_group][] = group_profile_basic_info|node|person_profile|form\nfeatures[field_group][] = group_sidebar_components|node|person_profile|form\nfeatures[field_instance][] = node-person_profile-field_address\nfeatures[field_instance][] = node-person_profile-field_contact\nfeatures[field_instance][] = node-person_profile-field_description\nfeatures[field_instance][] = node-person_profile-field_email\nfeatures[field_instance][] = node-person_profile-field_first_name\nfeatures[field_instance][] = node-person_profile-field_last_name\nfeatures[field_instance][] = node-person_profile-field_person_photo\nfeatures[field_instance][] = node-person_profile-field_phone_number\nfeatures[field_instance][] = node-person_profile-field_political_party\nfeatures[field_instance][] = node-person_profile-field_position_title\nfeatures[field_instance][] = node-person_profile-field_preferred_contact\nfeatures[field_instance][] = node-person_profile-field_profile_type\nfeatures[field_instance][] = node-person_profile-field_year_elected\nfeatures[node][] = person_profile\nfeatures[variable][] = comment_anonymous_person_profile\nfeatures[variable][] = comment_default_mode_person_profile\nfeatures[variable][] = comment_default_per_page_person_profile\nfeatures[variable][] = comment_form_location_person_profile\nfeatures[variable][] = comment_person_profile\nfeatures[variable][] = comment_preview_person_profile\nfeatures[variable][] = comment_subject_field_person_profile\nfeatures[variable][] = field_bundle_settings_node__person_profile\nfeatures[variable][] = menu_options_person_profile\nfeatures[variable][] = menu_parent_person_profile\nfeatures[variable][] = node_options_person_profile\nfeatures[variable][] = node_preview_person_profile\nfeatures[variable][] = node_submitted_person_profile\nfeatures[variable][] = pathauto_node_person_profile_pattern\nfeatures[variable][] = workbench_scheduler_person_profile\nfeatures[variable][] = xmlsitemap_settings_node_person_profile\nfeatures_exclude[field_instance][node-person_profile-field_components] = node-person_profile-field_components\nfeatures_exclude[field_instance][node-person_profile-field_sidebar_components] = node-person_profile-field_sidebar_components\n" ]

{ "pile_set_name": "Github" }

[ 0.0006339144215530904 ]

[ "est value? ", " (a) p (b) -3 (c) 1/3 (d) 5 (e) -0.05\nc\nLet l be (-2)/10 - 2783/(-1265). ", "Let y = -0.9 - 1.1. ", "What is the smallest value in 0.106, 0.4, y, l?", "\ny\nSuppose 0*m = -4*m - 9132. ", "Let s be -7*(-2)/77*(-25095)/2. ", "Let v = m - s. Which is the second smallest value? ", " (a) -1 (b) v (c) 4\na\nLet f(m) = m**3 + 95*m**2 - 820*m + 416. ", "Let q be f(-103). ", "Which is the fifth biggest value? ", " (a) 0 (b) 2 (c) q (d) 7 (e) -3\ne\nLet o = -4.564 - -4.064. ", "Let u = -114 + 105. ", "Suppose 4*d + 1 = 3*d. ", "What is the smallest value in d, u, o?", "\nu\nLet h = 71/1692 + 13/188. ", "Which is the fourth biggest value? ", " (a) 0.12 (b) 2 (c) h (d) -0.3\nd\nLet p = 69.59 + -65.4. ", "Let i = p - 2.19. ", "Which is the third smallest value? ", " (a) 1 (b) 20 (c) -1 (d) i\nd\nLet j be 4/((-20)/25) - 0. ", "Let r = 80 + -50. ", "Let w = -1506 + 1505. ", "Which is the third biggest value? ", " (a) r (b) j (c) w\nb\nLet j = -36 - -64. ", "Let t = 24 + j. Let p be (t/39 + (-2)/6)*-2. ", "Which is the third smallest value? ", " (a) p (b) 1/2 (c) -0.07\nb\nLet t = -0.0326 + 0.0726. ", "Let y = 0.7 + -0.56. ", "Let i = y - t. Which is the biggest value? ", " (a) i (b) 0 (c) -1 (d) -0.3\na\nLet i = 0.4 + -1.4. ", "Let o = 1/1637 + -1643/9822. ", "Which is the third smallest value? ", " (a) o (b) -0.02 (c) 0 (d) i\nb\nLet s = -45 + 44.8. ", "What is the biggest value in s, 1, -0.5, -1/230, 3?", "\n3\nLet a = 3.16 + -3. ", "Let t = -5.84 - a. Suppose 150*h - 364 = -214*h. ", "What is the fourth smallest value in -0.2, t, h, -2?", "\nh\nLet y be (-3542)/(-276) - (-52)/(-4). ", "Which is the biggest value? ", " (a) -0.0127 (b) 0 (c) y\nb\nLet f = -2679 - -2678.912. ", "Which is the second biggest value? ", " (a) -2 (b) 0.2 (c) f\nc\nLet u be 5 + -6 + (-15)/3. ", "Let v = -13 - u. Let x be 3/((-1)/4 + v/(-4)). ", "Which is the third biggest value? ", " (a) -0.5 (b) -9 (c) x\nb\nLet n = -3443/200 + 3/200. ", "Suppose 113 = 15*r + 83. ", "Which is the biggest value? ", " (a) n (b) 0.3 (c) r\nc\nLet m = 3792 - 3791.94. ", "What is the fourth smallest value in 2/11, 2, m, 0.1?", "\n2\nLet l(x) = -x**3 + 14*x**2 - 16*x + 29. ", "Let w = 431 - 418. ", "Let g be l(w). ", "Which is the biggest value? ", " (a) -0.5 (b) -4 (c) g (d) -0.9\na\nLet c = 3363 - 3363.013. ", "What is the second smallest value in 1, -1/3, c, 2, -0.1?", "\n-0.1\nSuppose -868 - 3596 = -1488*f. ", "Let z be (-22)/152 - (-1)/4. ", "Which is the third smallest value? ", " (a) f (b) -17/3 (c) z\na\nLet s = -9360 - -9378. ", "Which is the third biggest value? ", " (a) 0.2 (b) s (c) -11\nc\nLet y(u) = u**3 - 38*u**2 + 6*u - 61. ", "Let s be y(38). ", "Let q = -499/3 + s. What is the third smallest value in 0.4, q, 1/3?", "\nq\nLet i = -0.4 + -0.2. ", "Let v = 0.6 + i. Suppose -995 + 49 = -43*k. ", "Which is the fourth biggest value? ", " (a) 2/5 (b) k (c) v (d) -5\nd\nLet o be 12/(-26) + (-19720)/3016 + 50/6. ", "Which is the third biggest value? ", " (a) o (b) -8 (c) -3 (d) 58\nc\nLet h(o) = 3*o + 32. ", "Let k be h(-10). ", "Suppose k*z = -10, 3*z - 4*z = -4*g + 21. ", "Let c be ((-2)/g)/(3 - 2). ", "What is the third smallest value in 0.3, c, 0.5?", "\n0.5\nLet x = -7724/19185 + 10/3837. ", "Which is the third biggest value? ", " (a) 3/11 (b) -2/7 (c) x (d) -1 (e) 3/4\nb\nLet c = -0.2 - -0.2. ", "Let o(r) = r**2 - 8*r + 6. ", "Let l be o(7). ", "Suppose -11 + 65 = 50*p - 146. ", "What is the second biggest value in c, p, l?", "\nc\nLet f = -0.32 + 0.42. ", "Let y = -141 - -142. ", "Which is the second smallest value? ", " (a) -20/13 (b) y (c) f\nc\nLet s = 113.889 + -11.889. ", "Which is the third smallest value? ", " (a) -22 (b) -4 (c) s\nc\nLet c = -1.774 + 1.774. ", "Let g = -26.9 - -41.6. ", "Let o = g + -14. ", "What is the third biggest value in 0.1, o, c?", "\nc\nLet y be (-4)/10 + 7 + (-16)/(-15) + -9. ", "Which is the third biggest value? ", " (a) 0.23 (b) 3/5 (c) -0.5 (d) y\nc\nLet a = 1 + -1. ", "Let d = -0.19594 + 4.19594. ", "What is the third smallest value in -5, d, a, -0.4?", "\na\nLet x(y) = 28*y + 900. ", "Let u be x(-36). ", "Which is the biggest value? ", " (a) 8 (b) 2 (c) u\na\nSuppose -4*b - 257 = -s - 363, 3*s = -4*b + 130. ", "What is the third smallest value in 6, b, -1/3?", "\nb\nLet h be 98/34 + -3 + (-1760)/935. ", "What is the biggest value in 2/3, h, -8/29, -5, 3/7?", "\n2/3\nLet f = 225.7 + -226. ", "Let z = 70 + -69.5. ", "Which is the smallest value? ", " (a) z (b) f (c) -3/8 (d) -2/5\nd\nLet t = 400.7 + -7.7. ", "Let l = t - 418. ", "Which is the biggest value? ", " (a) 2 (b) -1/2 (c) l\na\nLet t = -1796 - -1796.5. ", "Which is the fifth smallest value? ", " (a) t (b) 11 (c) -2 (d) 0 (e) 5\nb\nLet v = -323 - -115. ", "Let s = v + 203. ", "Which is the third smallest value? ", " (a) 5 (b) s (c) -1 (d) -4\nc\nLet u = -0.2741 + 0.4741. ", "What is the second smallest value in -4, -1/37, 0.4, u?", "\n-1/37\nLet d = 7918 - 7918. ", "What is the biggest value in 43, 0.3, -3, -1/6, d?", "\n43\nLet z be (-4 + 10)*(1 - 2)/1. ", "Let q be z/20*-5 + 10/(-12). ", "Let p be 0 + 2 + (-20)/9. ", "What is the third biggest value in p, q, 7?", "\np\nLet p(o) = o**3 - 74*o**2 + 143*o + 61. ", "Let m be p(72). ", "Let s be 1/3 - (-5)/(-10). ", "Which is the biggest value? ", " (a) s (b) -5 (c) m\na\nLet v = -848.07 - -848. ", "What is the second biggest value in -23, 3, v, -3, 5?", "\n3\nLet x = 245 + -1716/7. ", "Let h = -913/8 - -114. ", "Which is the second biggest value? ", " (a) x (b) 24 (c) h (d) -1/5\nc\nLet a = -448 + 447.6. ", "Let f = 2.935 - -0.065. ", "What is the biggest value in a, f, -3, 0?", "\nf\nLet l = 19.7 + -19.6. ", "Which is the fourth biggest value? ", " (a) 12 (b) l (c) 0 (d) -0.3\nd\nLet y be (24/21)/(-4) + (-6334)/(-70). ", "Let m = 90 - y. Which is the fourth biggest value? ", " (a) m (b) 0.04 (c) -2 (d) 1\nc\nLet h = -65 + -31. ", "Let s = -96.5 - h. Which is the second smallest value? ", " (a) 0.3 (b) -8 (c) s\nc\nLet k = -2194 + 2194.3. ", "Which is the third biggest value? ", " (a) -0.348 (b) -1/4 (c) k (d) 4\nb\nLet h = 187 + -170. ", "Suppose -35 - 186 = -h*x. ", "What is the second biggest value in x, -0.06, -2?", "\n-0.06\nLet p = 1374.4 + -1374. ", "Let c = 1.1 + -6.1. ", "What is the biggest value in c, -1/9, p?", "\np\nLet l be 2/8 - (-2 + (-630)/8). ", "Suppose 2*p = -l - 117. ", "Let r be 216/p + (1 - -1). ", "Which is the third biggest value? ", " (a) r (b) 2/9 (c) 0.3\na\nLet k(g) = -2 - 2*g**2 + 17*g**2 + 2*g + 0 - g. Let l be k(1). ", "Let z = -97/74 + 30/37. ", "What is the second biggest value in -0.2, z, l?", "\n-0.2\nLet l = 12.5 + 767.5. ", "Let f = l + -779. ", "What is the fourth smallest value in 14, 2/15, f, -5?", "\n14\nLet v = -11515 + 57603/5. ", "Suppose -o + 2 - 4 = 0. ", "What is the second smallest value in 3, o, v?", "\n3\nLet l = -258 + 243. ", "Let j be (10/(-15))/(5/l*8). ", "Which is the third biggest value? ", " (a) -6 (b) 4/3 (c) j\na\nLet l = 272/655 - 2/131. ", "Let g = 214330 + -16716907/78. ", "Let h = 65/6 - g. What is the third smallest value in h, l, -1/8?", "\nl\nLet h = -1581 - -1580.94. ", "Which is the second biggest value? ", " (a) h (b) 19/5 (c) -14\na\nLet i = -89.7 - -90.1. ", "Which is the second smallest value? ", " (a) 1/8 (b) 0.5 (c) i (d) 1/18 (e) -2/41\nd\nSuppose 2*i + 35 - 30 = o, -3*o - 13 = i. Which is the fourth biggest value? ", " (a) -1/85 (b) 19 (c) i (d) -1\nc\nLet s = 26090 + -26022. ", "Which is the smallest value? ", " (a) -2 (b) s (c) -2/11 (d) 3 (e) -0.07\na\nLet i(n) = -16*n - 241. ", "Let x be i(-16). ", "Let h be (-20 + -20)*9/x. Which is the third biggest value? ", " (a) -7/3 (b) 1/6 (c) h\nc\nLet j be (-2 - -2)*(-2)/(2 + 2). ", "Suppose 0*d = d - 83. ", "Let l = d + -829/10. ", "What is the second biggest value in j, l, -5?", "\nj\nLet j = -5563 + 5567. ", "Which is the second biggest value? ", " (a) j (b) -19/3 (c) 0.3\nc\nLet j(v) = v**3 + 5*v**2 - v - 1. ", "Suppose y + 3 = 0, 4*u - y = 2*y - 11. ", "Let o be j(u). ", "Which is the second smallest value? ", " (a) -1 (b) -2/13 (c) o (d) 1\nb\nLet q = 28.03 + -28. ", "Let t = 0.47 + q. Let v = -17 - -15. ", "Which is the second biggest value? ", " (a) t (b) -0.2 (c) -1 (d) v\nb\nLet n = 323.6559 - 0.1559. ", "Let j = n - 324. ", "Which is the biggest value? ", " (a) j (b) -2/7 (c) -0.01 (d) -0.2\nc\nLet z = -12059 + 12059.4. ", "What is the smallest value in 0.05, z, -2/9, -3?", "\n-3\nLet f = 49017/2 - 24512. ", "Which is the third biggest value? ", " (a) 0.2 (b) f (c) 0 (d) 3\nc\nLet q be -11 + 0 - (44 - 50 - (4 + -1)). ", "Let y = -0.1 + -0.1. ", "Which is the third biggest value? ", " (a) -1 (b) y (c) q (d) 11\na\nSuppose -2*z + 3*r - 6 = -6*z, -z + 4*r + 11 = 0. ", "Suppose -z*k = -5 + 8. ", "What is the second smallest value in 0.17, k, 3?", "\n0.17\nLet t = 0.014 + 0.386. ", "Let n = 26 - 46. ", "Let q = n - -18. ", "Which is the third smallest value? ", " (a) 1 (b) t (c) q\na\nLet u = 6.6 - 1.6. ", "Let i = -915 + 918. ", "Which is the second smallest value? ", " (a) 2 (b) u (c) -0.6 (d) i\na\nLet q be (-3)/9 + (-5)/30. ", "Le" ]

{ "pile_set_name": "DM Mathematics" }

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[ "Q:\n\nHow to autotab after input of 1 or 2 decimal places in textbox vba?", "\n\nI want to move focus to next textbox after entering a value with lets say one decimal place eg. \"", "123.4\", as well it should not move if the value entered is text eg. \"", "abc.e\". ", "Is there any way?", "\n\nA:\n\nTest the next code, please:\nPrivate Sub TextBox1_Change()\n If Len(Me.", "TextBox1.Text) >= 3 Then\n If IsNumeric(Me.", "TextBox1.Text) And _\n Right(Me.", "TextBox1.Text, 3) Like \"#.#\" ", "Then\n 'controlX.SetFocus\n 'Me.txtTest.", "SetFocus\n End If\n End If\nEnd Sub\n\nUsing it together with the above event posted by @Siddharth Rout (not allowing other characters than numbers) should be the perfect solution for you, I think. ", "In such a case, IsNumeric(...) check can be missing.", "\nIf you need to make it allowing two decimal, it is enough to replace \"#.#\" ", "with \"#.##\" ", "and make Len(...) >= 4 and so on...\n\n" ]

{ "pile_set_name": "StackExchange" }

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[ "/* Mike Gertz - 2-Aug-98 */\n\n#ifndef SNFILEWRAPPER\n#define SNFILEWRAPPER\n#include \"snopt_PAGMO.h\"\n#ifdef __cplusplus\nextern \"C\" {\n#endif\n\n void snopenappend_ (integer *iunit, char *name,\n\t\t integer *inform, ftnlen name_len);\n\n void snfilewrapper_(char *name__, integer *ispec, integer *inform__,\n\t\t char *cw, integer *lencw, integer *iw,\n\t\t integer *leniw, doublereal *rw, integer *lenrw,\n\t\t ftnlen name_len, ftnlen cw_len);\n\n void snclose_ (integer *iunit);\n\n void snopenread_ (integer *iunit, char *name, integer *inform,\n\t\t ftnlen name_len);\n\n#ifdef __cplusplus\n}\n#endif\n\n#endif\n" ]

{ "pile_set_name": "Github" }

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[ "Q:\n\nWhy do so many godlike beings show up in TOS?", "\n\nFor maybe the first time, I'm more interested in a real-world answer. ", "In-universe, all that can really be said is that those \"godlike\" beings do exist, and Kirk and company crossed paths with them quite often.", "\nOut of universe, was this a favorite \"angle\" of Gene Roddenberry and the other writers? ", "Godlike beings in TOS seem to appear every other episode (Apollo, Melkotians, Trelane, Metrons, Organians, Guardian of Forever, \"Shore Leave\" aliens, Gary Mitchell, Thasians and Charlie Evans, Excalbians, Companion, Redjac, etc., ", "etc.).", "\n\nA:\n\nMost likely it was indeed. ", " It seems that Roddenberry took a dim view of most theistic beliefs, much as quite a few other humanists have done. ", " Here is a select quote attributed to Gene Roddenberry — culled from the Wikiquote page, I must admit.", "\n\nI think I’ve gone through quite an ordinary series of steps in life. ", "I began as most children began, with God and Santa Claus and the tooth fairy and the Easter Bunny all being about the same thing. ", "Then I went through the things that I think sensitive people go through, wrestling with the thoughts of Jesus—did he shit? ", "Did he screw? ", "I began to dare to believe that God wasn’t some white beard. ", "I began to look upon the miseries of the human race and to think God was not as simple as my mother said. ", "As nearly as I can concentrate on the question today, I believe I am God; certainly you are, I think we intelligent beings on this planet are all a piece of God, are becoming God. ", "In some sort of cyclical non-time thing we have to become God, so that we can end up creating ourselves, so that we can be in the first place. ... ", "My own feeling is that relation to God as a person is a petty, superstitious approach to the All, the infinite.", "\n\nAs quoted in God & (1975) by Terrance A. Sweeney\n\nSo far as Roddenberry's personal beliefs, whether described as atheism or pantheism, were concerned, that quote really exemplifies, I think, the characteristics we see with all the gods and god-like beings featured in the episodes of Star Trek. ", " It appears to me that the idea was to portray that being seen as a god, or god-like, does not necessitate such an entity genuinely be omnipotent, omniscient, or perfectly wise, et al.", "\n\n" ]

{ "pile_set_name": "StackExchange" }

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[ "Urinary tract stones: causes, complications and treatment.", "\nStones or calculi in the urinary tract affect up to 12% of men and 5% of women by the age of 70 years, with more than a third of individuals having a strong family history (Unwin, 1996). ", "Complications include obstruction in the urinary tract, pain, nausea, vomiting and sepsis. ", "Common causes are: urine stasis, infection, presence of foreign bodies, dehydration, diet and periods of immobility. ", "Encouraging initial diuresis could exacerbate rather than relieve symptoms. ", "Discharge advice is a key feature of preventing recurrence once the predisposing factors have been identified. ", "The relationship between patient and nurse is an invaluable and ideal opportunity for nurses to educate patients in appropriately changing dietary habit and in maintaining a urine output of greater than 2 litres per day." ]

{ "pile_set_name": "PubMed Abstracts" }

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[ "The First Circuit US Court of Appeals ruled today that the Defense of Marriage Act, that Clinton-era relic designed to defend the institution of marriage against gays like a football team defends the end zone (if the gays get into the marriage zone, game over for straights!), ", "is unconstitutional on the grounds that it…\n\nLast month homosexuals serving in the military won a huge battle in the fight for gay rights when Don't Ask, Don't Tell was repealed, and now they're taking on the other major federal policy that discriminates against gay people: The Defense of Marriage Act. ", "In a lawsuit filed today in Boston, a group of legally…\n\nGuys, these are really tough economic times, and according to legislators, we're all going to have to tighten our belts! ", "Unless of course, you're a high-priced lawyer who's helping Republicans discriminate against gays. ", "In that case, the House has $1.5 million with your name on it.", "\n\nThe Australian half of a couple married in Massachusetts is being deported, despite the fact that the Obama administration has stopped defending the Defense of Marriage Act and has urged discretion on deportations.", "\n\nFunny how these things work. ", "You may recall that the Republican-controlled House conveniently found $500,000 marked \"uphold a law that discriminates against gay people\" despite President Obama's declining to defend the Defense of Marriage Act in court. ", "That money went to a contact for a law firm, much to Democrats'…\n\nThe U.S. Citizenship and Immigration Services is not known for its rapid responsiveness, but that's belied by its announcement recently that same-sex partners of citizens won't automatically be denied green cards, now that the Obama administration has announced it won't fight for the Defense of Marriage Act.", "\n\nHawaii's governor signed a bill into law yesterday legalizing civil unions for gay and straight couples in his state, marking another step forward for gay rights. ", "But Obama's still \"grappling\" with his feelings on gay marriage.", "\n\nThe Obama Justice Department has announced it will no longer fight for the Defense of Marriage Act in court. ", "Gay rights advocates had long been infuriated that despite the administration's opposition to it, government lawyers were still defending in court the act that prohibits federal recognition of gay marriage.", "\n\nThe past 24 hours are typical of the strange, complex position of gay rights today: On the same day of a judge's injunction blocking Don't Ask, Don't Tell, the Obama administration appealed on behalf of the Defense of Marriage Act.", "\n\nNow that the so-called \"Defense of Marriage\" act has been declared unconstitutional, I've made some maps to show everyone where we stand right now in terms of marriage equality rights — and, of course, our right to marry guinea pigs.", "\n\nA Massachusetts district court judge sided with Massachusetts' argument that the Defense of Marriage Act requires discrimination against its own citizens. ", "The Justice Department had argued that the federal government \"has the right to set eligibility requirements for federal benefits.\"", "\n\nMassachusetts Attorney General Martha Coakley is challenging the Defense of Marriage Act, arguing that it violates Massachusetts' right to regulate marriage as it sees fit. ", "Several Massachusetts couples filed an equal protection suit again DOMA in March. [", "Boston Globe]" ]

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[ "1982 East Texas State Lions football team\n\nThe 1982 East Texas State Lions football team represented East Texas State University in the 1982 NCAA Division II football season. ", "They were led by head coach Ernest Hawkins, who was in his 18th season at East Texas State. ", "The Lions played their home games at Memorial Stadium and were members of the Lone Star Conference. ", "The Lions finished tied for second in the Lone Star Conference. ", "This was also their first year as members of the NCAA, as ETSU and the Lone Star Conference had ended its association with the N.A.I.A.\n\nSchedule\n\nPostseason Awards\n\nAll-Americans\nKyle Mackey, Honorable Mention Quarterback\n\nAll-Lone Star Conference\n\nLSC First Team\nBen Boston, Defensive Back\nRicky Dirks, Running Back \nKyle Mackey, Quarterback \nPeter Roos, Offensive Tackle\n\nLSC Second Team\nJavier Cardenas, Tight End \nDavid Lowe, Defensive End \nBurl Perry, Center\n\nLSC Honorable Mention\nChris Flynn, Defensive Back\nRandy Jones, Punter\nKevin Rush, Linebacker \nVaughn Williamson, Offensive Guard\n\nReferences\n\nEast Texas State\nCategory:Texas A&M–Commerce Lions football seasons\nEast Texas State Lions football" ]

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[ "Q:\n\nProperty binding updates an event frame later\n\nI have a C++ object exposed to QML as myObject. ", "This C++ object has a Q_PROPERTY:\nQ_PROPERTY (bool myProperty READ getMyPropert NOTIFY myPropertyChanged)\nIn QML I use this as a guard in a SignalTransition as follows:\nproperty bool foo: myObject.myProperty\n\nSignalTransition {\n targetState: someState\n signal: someSignal\n onTriggered: console.info(\"foo: \" + foo)\n onTriggered: console.info(\"myObject.myProperty: \" + myObject.myProperty)\n}\n\nThe output is the following:\nfoo: false\nmyObject.myProperty: true\n\nAn event frame later, foo becomes true as well.", "\nIs this behaviour normal?", "\nEDIT: \nHere is a working example:\nMyClass.h:\n#pragma once\n\n#include <QObject>\n\nclass MyClass : public QObject {\nQ_OBJECT\n\n Q_PROPERTY(bool myProperty_1 READ getMyProperty_1 NOTIFY myClassChanged)\n Q_PROPERTY(bool myProperty_2 READ getMyProperty_2 NOTIFY myClassChanged)\n\npublic:\n static void initQML();\n\n MyClass();\n\n bool getMyProperty_1();\n bool getMyProperty_2();\n\n Q_INVOKABLE void setMyProperty(bool value);\n\nsignals:\n void myClassChanged();\n\nprivate:\n bool m_MyProperty_1;\n bool m_MyProperty_2;\n};\n\nMyClass.cpp:\n#include \"MyClass.h\"\n\n#include <QtQml>\n#include <QDebug>\n#include <QMetaType>\n\n/*static*/ void MyClass::initQML() {\n qmlRegisterType<MyClass>(\"Test\", 1, 0, \"MyClass\");\n}\n\nMyClass::MyClass() : m_MyProperty_1(false), m_MyProperty_2(false) {\n qDebug() << \"Constructor called.\";", "\n}\n\nbool MyClass::getMyProperty_1() {\n return m_MyProperty_1;\n}\n\nbool MyClass::getMyProperty_2() {\n return m_MyProperty_2;\n}\n\nvoid MyClass::setMyProperty(bool value) {\n m_MyProperty_1 = value;\n m_MyProperty_2 = value;\n myClassChanged();\n}\n\nmain.cpp:\n#include <QGuiApplication>\n#include <QQmlApplicationEngine>\n\n#include \"MyClass.h\"\n\nint main(int argc, char *argv[])\n{\n QGuiApplication::setAttribute(Qt::AA_EnableHighDpiScaling);\n\n QGuiApplication app(argc, argv);\n\n // Init\n\n MyClass::initQML();\n\n // Main loop\n\n QQmlApplicationEngine engine;\n engine.load(QUrl(QStringLiteral(\"qrc:/main.qml\")));\n\n return app.exec();\n}\n\nmain.qml:\nimport QtQuick 2.9\nimport QtQuick.", "Controls 2.2\n\nimport QtQml.", "StateMachine 1.0 as QtQml_StateMachine\n\nimport Test 1.0\n\nApplicationWindow {\n visible: true\n\n width: 480\n height: 272\n\n Component.onCompleted: _stateMachine.start()\n\n // UI\n\n Button {\n text: \"Switch\"\n\n onClicked: {\n console.info(\"Switch pressed with setter\")\n myClass.setMyProperty(true)\n }\n }\n\n // StateMachine\n\n property MyClass myClass: MyClass {}\n\n QtQml_StateMachine.", "StateMachine {\n id: _stateMachine\n\n initialState: _defaultState\n\n onStarted: console.info(\"_stateMachine started\")\n onExited: console.info(\"_stateMachine exited\")\n\n QtQml_StateMachine.", "State {\n id: _defaultState\n\n property bool myProperty_1: myClass.myProperty_1\n property bool myProperty_2: myClass.myProperty_2\n\n onMyProperty_1Changed: console.info(\"onMyProperty_1Changed: \" + myProperty_1)\n onMyProperty_2Changed: console.info(\"onMyProperty_2Changed: \" + myProperty_2)\n\n onEntered: console.info(\"_defaultState entered\")\n onExited: console.info(\"_defaultState exited\")\n\n // Doesn't work:\n QtQml_StateMachine.", "SignalTransition {\n targetState: _nextState\n signal: _defaultState.myProperty_1Changed\n guard: _defaultState.myProperty_2\n onTriggered: console.info(\"myProperty_2\")\n }\n\n // Works:\n// QtQml_StateMachine.", "SignalTransition {\n// targetState: _nextState\n// signal: _defaultState.myProperty_1Changed\n// guard: myClass.myProperty_2\n// onTriggered: console.info(\"myClass.myProperty_2\")\n// }\n }\n\n QtQml_StateMachine.", "State {\n id: _nextState\n\n onEntered: console.info(\"_nextState entered\")\n onExited: console.info(\"_nextState exited\")\n }\n }\n}\n\nIf you use the commented SignalTransition it works. ", "If you use the other one it won't work.", "\n\nA:\n\nThe issue is that there is a race condition, due to proxying the C++ object's properties to have individual Changed signals. ", "This is due to the direct connections in QML.", "\nThe update works in the following order:\nmyClassChanged -> set: m_MyProperty_1 (C++) -> signal myProperty_1Changed (QML) -> transition and hit the guard, then -> set: m_MyProperty_2 (C++) -> signal m_MyProperty_2Changed (QML)\nso myProperty_1 racing against myProperty_2.", "\n\n" ]

{ "pile_set_name": "StackExchange" }

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[ "Antimicrobial resistance of Campylobacter spp. ", "isolated from broiler flocks in Iceland 2001-2005.", "\nMinimum inhibitory concentrations of six antimicrobial agents were determined for one Campylobacter sp. ", "isolate from each of the 362 Campylobacter-positive commercial chicken flocks in Iceland in the years 2001-2005. ", "Of all isolates tested, 6.9% were resistant, although none were multiresistant. ", "Resistance to ampicillin was most commonly observed (3.6%) followed by resistance to enrofloxacin (3%), nalidixic acid (1.9%), and oxytetracyclin (0.3%), with cross-resistance between enrofloxacin and nalidixic acid. ", "All isolates were susceptible to erythromycin and gentamicin. ", "Resistance rates among Campylobacter coli isolates (7/13 or 53.8%) were much higher than among Campylobacter jejuni isolates (18/349 or 5.2%), and resistance patterns differed. ", "Resistant strains were compared using pulsed field gel electrophoresis. ", "Macrorestriction with SmaI and KpnI restriction enzymes yielded 13 different pulsotypes, none of which indicated a predominant genotype. ", "Specific pulsotypes with uniform resistance patterns arising on geographically separated farms indicate clonal dissemination. ", "Although resistance levels were low and similar to that seen in the other Nordic countries, further research on this matter is needed as there is no antimicrobial selective pressure in chicken farming in Iceland." ]

{ "pile_set_name": "PubMed Abstracts" }

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{ "pile_set_name": "PubMed Central" }

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[ "/*\n * Licensed to the Apache Software Foundation (ASF) under one or more\n * contributor license agreements. ", " See the NOTICE file distributed with\n * this work for additional information regarding copyright ownership.", "\n * The ASF licenses this file to You under the Apache License, Version 2.0\n * (the \"License\"); you may not use this file except in compliance with\n * the License. ", " You may obtain a copy of the License at\n *\n * http://www.apache.org/licenses/LICENSE-2.0\n *\n * Unless required by applicable law or agreed to in writing, software\n * distributed under the License is distributed on an \"AS IS\" BASIS,\n * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.", "\n * See the License for the specific language governing permissions and\n * limitations under the License.", "\n */\npackage org.apache.commons.vfs2.provider.http4s;\n\nimport org.apache.commons.vfs2.provider.", "FileNameParser;\nimport org.apache.commons.vfs2.provider.", "GenericURLFileNameParser;\n\n/**\n * {@code FileNameParser} implementation for http4s provider, setting default port to 443.", "\n *\n * @since 2.3\n */\npublic class Http4sFileNameParser extends GenericURLFileNameParser {\n\n private static final int DEFAULT_PORT = 443;\n\n private static final Http4sFileNameParser INSTANCE = new Http4sFileNameParser();\n\n public Http4sFileNameParser() {\n super(DEFAULT_PORT);\n }\n\n public static FileNameParser getInstance() {\n return INSTANCE;\n }\n}\n" ]

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[ "Discrete distributions of putative cholinergic and somatostatinergic amacrine cell dendrites in chicken retina.", "\nThe distributions of putative cholinergic and somatostatinergic amacrine cells of the chicken retina were compared. ", "Acetylcholinesterase-positive amacrine cell bodies were concentrated at the border between the inner nuclear and plexiform layers. ", "Similar amacrine cell bodies were detected in a displaced position in the ganglion cell layer. ", "Both populations had dendrites joining the 4 bands of acetylcholinesterase activity in the inner plexiform layer. ", "The cell bodies of somatostatin-immunoreactive amacrine cells were distinct from the intensely acetylcholinesterase-positive cell bodies. ", "The immunoreactive terminal bands did not overlap the acetylcholinesterase-positive bands, except in the inner parts of the inner plexiform layer." ]

{ "pile_set_name": "PubMed Abstracts" }

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[ " \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \nsubscribe to my channel\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \nthank you for watching my video\ndon't forget to like, comment and subscribe\n \n" ]

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[ "The Radiobiological Standardization Core will provide standardized radiobiology tests for all projects within the CMCR with respect to tissue culture assays, animal model assays in the mouse and Zebrafish to ensure uniformity, reproducibility, and statistical significance of all radiobiological tests. ", "The Radiobiological Standardization Core will function to deliver three specific aims: Aim 1: Ensure standardized in vitro cell culture, DNA damage quantitation, and comparative analysis of radioprotective and radiation mitigating functions of all new products developed by the five projects within the CMCR. ", "Aim 2: Deliver timely reports and provide rapid analysis of cell culture and animal responses to new drugs developed by the five projects. ", "Aim 3: Determine whether the Zebrafish represents an accurate, rapid, and inexpensive alternative to mouse assays for screening new radiobiological protectors and mitigators. ", "The Radiobiological Standardization Core has as a main goal: the relief of the five projects from the diluted effort of doing their own tissue culture and animal model analysis of new products. ", "By standardization of in vitro and in vivo radiation biology testing in this core facility, the five projects should be able to focus on the critical task of interaction between chemistry and radiation biology for drug discovery and development." ]

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[ "Unless rural incomes, hit by demonetisation, are revived, consumer demand is not going to grow\n\nTo pull India out of the current economic slowdown, the government can loosen its purse strings, make pending payments, give GST refunds quickly, and revamp MGNREGA to put more money in the hands of rural consumers, Ajit Ranade, Chief Economist at the Aditya Birla Group, and Pronab Sen, former Chief Statistician of India, tell TCA Sharad Raghavan. ", "They add that we can expect to see the slowdown lasting for a few more quarters. ", "Edited excerpts from a conversation:\n\nDr. Sen, do you think we are in a slowdown? ", "And if we are, is it more structural, in that we need to make drastic changes, or is it more cyclical, where if we just make smaller changes we can ride out the storm?", "\n\nPronab Sen: We are in a slowdown. ", "There is no question about it. ", "And I think we have only seen the first phase of the slowdown. ", "It has been five quarters now and I think it will go on for at least a couple of quarters more, maybe longer than that. ", "To my mind, the problem is essentially structural, but structural does not necessarily mean that you have to do deep reforms to get over it. ", "What you have to do is identify the cause of the structural slowdown and address it directly. ", "Indirect instruments don’t work in the case of structural constraints.", "\n\nDr. Ranade, of the main drivers of the economy — government expenditure, private consumption, investment, and exports — which of them do you feel need a revival most urgently?", "\n\nAjit Ranade: I agree with Pronab that we are in a slowdown and I believe this is a problem of lack of aggregate demand. ", "This is a slowdown not because we are not able to produce enough or that we have run out of capacity to produce; it is because there is not enough demand. ", "You identified the four sources of demand. ", "Of course the most sustainable and long-term solution to come out of the slowdown is when investment demand picks up, especially from private investment spending. ", "But that is not something that can happen in a jiffy because it requires the investor’s confidence, it requires investors to take risks.", "\n\nSo, in the near term, because exports depend on the enthusiasm of foreigners buying Indian goods, maybe some supply-side measures like trade facilitation, removing bottlenecks, reducing the GST refund period delay, or even managing the exchange rate [may work], but fundamentally if the global slowdown is a reality, then export demand cannot pick up quickly. ", "Although, I do believe that India’s share of manufacturing exports in the world is barely 2% or something, so we can easily go from 2% to 3%. ", "In the near term I think the aggregate demand gap has to be filled in by some kind of government spending, although we can have a separate discussion on the fiscal situation. ", "But I believe that’s what is required.", "\n\nDr. Sen, Dr. Ranade has identified the most important driver that needs to be revived, but if we are looking for low-hanging fruit, if the government were to do something quickly that would have the biggest impact, what do you think that could be?", "\n\nPS: I think Ajit and I agree. ", "The problem is really private consumption demand. ", "Remember that the government has limited instruments in its hands. ", "It cannot stimulate private consumption directly, except in certain ways. ", "But the focus needs to be primarily on that. ", "The things that Ajit talked about in terms of exports would have to be in terms of trade facilitation and issues of that kind, and a sensible exchange rate policy, which we don’t have at the moment. ", "The focus really would have to be on how to do you revive consumption demand. ", "To my mind, the first step is really to go back to something we briefly touched on, which is the fiscal deficit.", "\n\nIf you were to ask me what I would recommend, I would say the first thing I would recommend is please recognise that the true fiscal deficit is significantly above the reported fiscal deficit. ", "Because the outcome of trying to suppress your fiscal deficit artificially is that the government is not paying its dues. ", "It is not giving refunds; export credit refund is a large issue. ", "But this is true of GST refunds across the board. ", "The second is that the government is not paying off its suppliers. ", "The third is that a lot of government spending that has already been budgeted for and announced has not being made. ", "PM KISAN is still languishing. ", "These are things which have been budgeted for but that money has not been spent or has not been shown to be spent, simply because the government is not releasing the requisite funds. ", "Just recognise the fiscal deficit for what it is and put the money out, then we can go back to the serious issue of correcting the fiscal deficit over the next few years.", "\n\nDr. Ranade, the government has recently announced certain steps to release some of these locked up funds. ", "It is saying that within a time-bound period, we will pay our suppliers, and GST input tax refunds will be credited in a short window. ", "Does this mean that the government will then have to cut down on other spending or can it keep the fiscal deficit target and say that we’ll do both — we’ll increase our spending and we’ll give all of these pending payments?", "\n\nAR: I am going to ask for forgiveness from god, and Pronab, and all my colleagues. ", "I am going to stick my neck out and say that this is a time when we need to actually worry less about the fiscal deficit target. ", "After all, 3% or 3.3%, there is no golden rule. ", "I want to emphasise what Pronab said: even the routine stuff, the clearing payments which are not in dispute, where the vendors have supplied their services or goods, that itself is a very huge number if you count State and Central governments. ", "I think it is very large, about ₹10 lakh crore. ", "Just releasing this payment or making very quick refunds for exporters, especially SMEs, who have to pay 28% GST and then claim a refund would help a lot. ", "So, that is the easier thing to do, and I would recommend that we don’t get hung up on the deficit, even though the CAG said that the 3.3% reported is not the right number. ", "The actual deficit at the Central government level may be as high as 5.5% and when you factor in the State governments, the combined deficit could be 8-8.5%.", "\n\nBut remember that the nominal GDP growth rate has dropped to 8% and we are in a very unusual and unprecedented situation of low inflation and low GDP growth in nominal terms, so this is the time when we have to take the risk of cyclical fiscal expansion. ", "One thing I would like to mention, which Pronab also mentioned, is that purchasing power, especially in rural areas, is of prime importance. ", "So, the driver of growth we need to look at is government spending, but also consumption in rural areas which is going to be helped by things like MGNREGA and wage growth because that will also require fiscal expansion.", "\n\nDr. Sen, there were reports on how the government is considering pegging MGNREGA payments to an updated CPI inflation. ", "Do you feel this will have a big impact in terms of putting more money in the hands of rural workers?", "\n\nPS: MGNREGA wages in any case were inflation indexed. ", "What the government has announced is that it will be linked to the CPI for agricultural labour or the rural CPI, whichever shows more inflation. ", "That’s all they have done. ", "It’s been indexed all along, nothing new in that.", "\n\nWhether this is going to have an effect will depend entirely on how well MGNREGA is being implemented. ", "The fact of the matter is that over the past five years or so, the confidence of State governments that the Central government will pay up the MGNREGA funds has eroded significantly. ", "And the net result is a lot of State governments simply haven’t been putting the same level of commitment in MGNREGA as they used to. ", "Over the years MGNREGA has become a a supply-based system from a demand-based system. ", "The State government says, I have got a public work, now you guys want to work on it, you can come and work on it. ", "Earlier, it used to be a system where people went and demanded work and the State government was bound to give it to them and the Central government was bound to refund the labour cost of that particular project. ", "So, unless you redesign MGNREGA to its original form, just indexing the wages is not going to do a whole lot.", "\n\nNow that we have identified private consumption as one major driver that needs to be revived, what are the ways, Dr. Ranade, that we can put more money in people’s hands? ", "Are income tax rate cuts viable and will they be effective?", "\n\nAR: Let’s not forget that a big driver of growth is consumption, which includes rural consumption. ", "And so, I want to reiterate what Pronab said about MGNREGA. ", "Make it truly demand-driven, make the wage indexation meaningful and involve social audits which were successful in some States like Andhra and Rajasthan. ", "Involve social audits to ensure effectiveness, and also focus on the dual objective of asset creation wherever possible. ", "But primarily it should be about putting some income in the hands of rural consumers.", "\n\nI am going to propose a radical suggestion. ", "Since we also agreed that some of the reasons for the slowdown are structural, I believe one of the big structural features of the Indian economy right now is the massive drop in female labour force participation. ", "In the last 10 or 12 years, it has come down by 10 percentage points, from 30-32% to 22%, which means that only one out of five working age women are actually working for a paid job. ", "So, here’s my radical suggestion: Think of a 10-year or 15-year completely tax-free income for women. ", "That is zero income tax for all women. ", "That’s a suggestion to also increase consumption but it would be mainly to encourage paid jobs for women.", "\n\nDr. Sen, is it accurate to say that this slowdown that we are seeing is the delayed effect of demonetisation and that has completely removed the parallel economy?", "\n\nPS: Yes, unquestionably so. ", "The unorganised sector has been hit now for a long time and unless rural incomes are revived, and that is where 70% of our population is, consumer demand is not going to grow. ", "So, what we are talking about is the same, that the principal cause of distress in rural areas was demonetisation. ", "If you want to fix that structural break, you need to bring back rural income to some semblance of normalcy.", "\n\nDr. Ranade, do you agree?", "\n\nAR: Yeah, 90% of India’s labour force is in the informal sector. ", "We have to recognise that this is the normality of the Indian economy and, therefore, whatever disrupts that, we are disrupting the mainstream. ", "And that I believe is the lingering effect of demonetisation. ", "I believe the rural wages, which used to grow at perhaps 10-15% a year, have grown at barely 1% in the last few years. ", "And this has certainly affected rural purchasing power." ]

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[ "In vitro study of the influence of virginiamycin and spiramycin on the composition and biochemical activities of the gastrointestinal flora of piglets. ", "II. ", "Influence on the biochemical activities of the microflora.", "\nChemical analysis was carried out on 54 in vitro fermentations to study the influence of nutritional doses of Virginiamycin and Spiramycin on the metabolic activity of the gastro-intestinal flora of 18 in vivo treated piglets. ", "Changes in the decomposition of glucose and the production of NH3, volatile acids and lactic acid are recorded in function of time. ", "These results are in good accordance with changes noted in the composition of the bacterial flora, such as a marked decrease in the production of lactic acid, caused by Virginiamycin, combined with a decrease in the number of Lactobacilli and Enterococci. ", "Virginiamycin caused marked changes in the metabolic activity of certain groups of bacteria, while there was only a slight effect noted for Spiramycin, although in vivo treatments with this antibiotic still show up in the results of the in vitro incubations. ", "The overall results indicate that both antibiotics have marked influences on the intestinal flora of the pig, either by selective inhibiting of the flora resulting in a change of the metabolities formed, either by a change in the metabolic activity of some bacterial groups." ]

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[ "Cantharellopsis\n\nCantharellopsis is a tan- to whitish-colored bryophilous monotypic genus in the Agaricales. ", "The fruit bodies of the single species Cantharellus prescotii has a form intermediate between an Omphalina and a chanterelle (Cantharellus) because of its forked, fold-like gills. ", "It inhabits moss on calcareous soils in temperate regions of Europe. ", "Phylogenetically related agarics are in the genera Contumyces, Gyroflexus, Loreleia, Rickenella and Blasiphalia, as well as the stipitate-stereoid genera Muscinupta and Cotylidia and the clavarioid genus, Alloclavaria.", "\n\nEtymology\n\nCantharellopsis is named in reference to its vague similarity to the genus Cantharellus and means, Cantharellus-like.", "\n\nSee also\n\nList of Agaricales genera\n\nReferences\n\nExternal links\nImage\n\nCategory:Repetobasidiaceae\nCategory:Monotypic Agaricales genera\nCategory:Fungi of Europe" ]

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[ "Menu\n\nNew Year’s Food 101: Morimono\n\nI’m not sure what the symbolism of this arrangement of items are or even if it’s from Japan. ", "I know that this is a local Hawaii custom from plantation days so we do it too. ", "The items, from left to right are yoken (sweet bean paste), kamaboko (it should be green, but this pink one had a matsu in it which was cool), and I have gobo (long llife) tempura. ", "I’m also supposed to have tangerine slices (but people wanted to take the tangerines home) and kanten (red and green agar). ", "KTA had the kanten, but I think it’s kind of gross, and after paying $10 for one block of yokan (!), ", "I was not about to pay for the two blocks of kanten, especially since I’m not sure what this is for besides to make pretty. ", "If somebody knows, please inform me." ]

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[ "using Ben.", "Diagnostics;\nusing Microsoft.", "AspNetCore.", "Builder;\nusing Microsoft.", "AspNetCore.", "Hosting;\nusing Microsoft.", "AspNetCore.", "Http;\nusing Microsoft.", "Extensions.", "Configuration;\nusing Microsoft.", "Extensions.", "DependencyInjection;\nusing Microsoft.", "Extensions.", "Hosting;\n\nnamespace AspNetCoreRateLimit.", "Demo\n{\n public class Startup\n {\n public Startup(IConfiguration configuration)\n {\n Configuration = configuration;\n }\n\n public IConfiguration Configuration { get; }\n\n // This method gets called by the runtime. ", "Use this method to add services to the container.", "\n public void ConfigureServices(IServiceCollection services)\n {\n // needed to load configuration from appsettings.json\n services.", "AddOptions();\n\n // needed to store rate limit counters and ip rules\n services.", "AddMemoryCache();\n\n // configure ip rate limiting middle-ware\n services.", "Configure<IpRateLimitOptions>(Configuration.", "GetSection(\"IpRateLimiting\"));\n services.", "Configure<IpRateLimitPolicies>(Configuration.", "GetSection(\"IpRateLimitPolicies\"));\n services.", "AddSingleton<IIpPolicyStore, MemoryCacheIpPolicyStore>();\n services.", "AddSingleton<IRateLimitCounterStore, MemoryCacheRateLimitCounterStore>();\n\n // configure client rate limiting middleware\n services.", "Configure<ClientRateLimitOptions>(Configuration.", "GetSection(\"ClientRateLimiting\"));\n services.", "Configure<ClientRateLimitPolicies>(Configuration.", "GetSection(\"ClientRateLimitPolicies\"));\n services.", "AddSingleton<IClientPolicyStore, MemoryCacheClientPolicyStore>();\n //services.", "AddSingleton<IRateLimitCounterStore, MemoryCacheRateLimitCounterStore>();\n\n var opt = new ClientRateLimitOptions();\n Configuration.", "GetSection(\"ClientRateLimiting\").Bind(opt);\n\n services.", "AddMvc((options) => \n {\n options.", "EnableEndpointRouting = false;\n\n }).AddNewtonsoftJson();\n\n // https://github.com/aspnet/Hosting/issues/793\n // the IHttpContextAccessor service is not registered by default.", "\n // the clientId/clientIp resolvers use it.", "\n services.", "AddSingleton<IHttpContextAccessor, HttpContextAccessor>();\n\n // configure the resolvers\n services.", "AddSingleton<IRateLimitConfiguration, RateLimitConfiguration>();\n }\n\n // This method gets called by the runtime. ", "Use this method to configure the HTTP request pipeline.", "\n public void Configure(IApplicationBuilder app, IWebHostEnvironment env)\n {\n app.", "UseBlockingDetection();\n\n app.", "UseIpRateLimiting();\n app.", "UseClientRateLimiting();\n\n if (env.", "IsDevelopment())\n {\n app.", "UseDeveloperExceptionPage();\n }\n else\n {\n // The default HSTS value is 30 days. ", "You may want to change this for production scenarios, see https://aka.ms/aspnetcore-hsts.", "\n app.", "UseHsts();\n }\n\n app.", "UseHttpsRedirection();\n\n app.", "UseMvc();\n }\n }\n}" ]

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[ "\n825 F.Supp. ", "860 (1993)\nCharles E. JONES, Petitioner,\nv.\nIllinois Attorney General Roland BURRIS, et al., ", "Respondents.", "\nNo. ", "93 C 1981.", "\nUnited States District Court, N.D. Illinois, E.D.\nJune 30, 1993.", "\nCharles E. Jones, plaintiff pro se.", "\nNo appearance filed.", "\n\n\n*861 MEMORANDUM OPINION AND ORDER\n\nSHADUR, Senior District Judge.", "\nCharles Jones (\"Jones\") has presented a self-prepared Petition for Writ of Mandamus (the \"Petition\") seeking relief against Illinois Attorney General Roland Burris and the clerks of the Illinois Supreme Court and the Circuit Court of Cook County. ", "Jones asks that those defendants be compelled to provide him with access to trial court records in two Circuit Court criminal cases that Jones contends are needed \"to perfect a fair appellate brief.", "\"[1]\nAccording to the Petition Jones filed a pro se notice of appeal in those state court cases on December 3, 1991. ", "Jones' filings with this Court (the Petition together with later-filed documents) reflect that the state court has appointed counsel to represent Jones in his appeal. ", "Appointed counsel has received certain portions of the trial record, but Jones contends that the record provided to him is incomplete. ", "In addition, Jones maintains that the transcript of a January 16, 1991 hearing in one of his cases does not truly and accurately reflect the proceedings transcribed and contains falsifications.", "\nThere are several basic defects in the Petition, any one of which would require its denial. ", "In combination they are unquestionably fatal to Jones' action.", "\nFirst of all, Jones' selection of mandamus as a remedy fails because a federal district court has no general mandamus jurisdiction to compel action by state court officials (see, e.g., Davis v. Lansing, 851 F.2d 72, 74 (2d Cir.1988); Van Sickle v. Holloway, 791 F.2d 1431, 1436 n. 5 (10th Cir.1986)). ", "To be sure, because Jones alleges that defendants' actions have violated his federal constitutional rights, this Court might instead treat the Petition as a complaint seeking injunctive relief under 42 U.S.C. § 1983 (\"Section 1983\").[2] But such a transformation would not benefit Jones, for his claim that the state has not provided him with a record of sufficient completeness and accuracy to ensure a fair appellate review of his convictions is at heart an attack on the legality of his custody. ", "Indeed, Jones himself recognizes that in his May 17, 1993 Request for Decision where he \"avers that, the relief sought is crucial, in that the relief sought would have a direct bearing on the constitutionality of an `unjust, and illegal incarceration.'\" ", "Habeas corpus, with its concomitant exhaustion-of-state-remedies requirement, is the exclusive federal remedy for a state prisoner to challenge the validity of his conviction (Preiser v. Rodriguez, 411 U.S. 475, 500, 93 S.Ct. ", "1827, 1841, 36 L.Ed.2d 439 (1973)). ", "Consequently an inmate may not maintain a Section 1983 suit seeking injunctive relief solely to facilitate an attack on a conviction in state court proceedings (Scruggs v. Moellering, 870 F.2d 376, 378-79 (7th Cir.1989)). ", "Because Jones clearly has yet to exhaust his state court remedies, any federal consideration of his claims is premature.", "\nHence the Petition is legally frivolous in the sense that it lacks any arguable legal basis for a federal claim (Neitzke v. Williams, 490 U.S. 319, 109 S.Ct. ", "1827, 104 L.Ed.2d 338 (1989)), and this Court denies Jones' motion for leave to file in forma pauperis (id.). ", "In accordance with the procedure prescribed by Denton v. Hernandez, ___ U.S. ___, ___ 112 S.Ct. ", "1728, 1734, 118 L.Ed.2d 340 (1992), this action is dismissed without prejudice pursuant to 28 U.S.C. § 1915(d). ", "In addition Jones is informed:\n1. ", "If he wishes to appeal this order of dismissal, within 30 days after the entry of judgment he must file a Notice of Appeal to the United States Court of Appeals for the Seventh Circuit (see Fed.", "R.App.", "P. 4(a)). ", "That Notice of Appeal must be filed with the Clerk of the Court of the United States District Court, 219 South Dearborn Street, 20th Floor, Chicago, Illinois 60604.", "\n\n*862 2. ", "Although this Court of course expresses no substantive views on this subject, Jones should also be aware that if the Court of Appeals were to determine that such an appeal were \"frivolous\" in the legal sense, that could result in the imposition of sanctions by that Court (see Fed.", "R.App.", "P. 38).", "\nNOTES\n[1] For the reasons explained in this opinion, it proves unnecessary to determine which of the defendants would be the appropriate party or parties capable of providing the relief that Jones seeks — if he could properly obtain such relief in this case (as he cannot).", "\n[2] That type of reading would comport with the liberal-reading mandate of Haines v. Kerner, 404 U.S. 519, 520-21, 92 S.Ct. ", "594, 595-96, 30 L.Ed.2d 652 (1972) (per curiam).", "\n" ]

{ "pile_set_name": "FreeLaw" }

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[ "Ez volt Róma legnagyobb arénája, 250 ezer nézőre tervezték. ", "Zajlottak itt állatviadalok, a Ben Hur című filmben látható kocsiversenyek, de előfordult, hogy tengeri csatákat játszottak el hajókkal. ", "Elmondhatjuk, hogy ez volt az ókori Hollywood.", "\n\nMost virtuális szemüveg segítségével nézhetjük meg, milyen lehetett fénykorában. ", "A projekt, a római önkormányzat és a GSNET vállalat közös munkája a legnagyobb kültéri virtuális valóságélmény lesz.", "\n\nA Circus Maximusban csak szeptember végéig élvezhetjük ókori Róma illúzióját, ha lemaradtunk róla, már csak a 2021-es turistaszezonban tudjuk kipróbálni – írta a Euronews." ]

{ "pile_set_name": "OpenWebText2" }

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[ "Leptin receptors in human skeletal muscle.", "\nHuman skeletal muscle expresses leptin receptor mRNA; however, it remains unknown whether leptin receptors (OB-R) are also expressed at the protein level. ", "Fourteen healthy men (age = 33.1 +/- 2.0 yr, height = 175.9 +/- 1.7 cm, body mass = 81.2 +/- 3.8 kg, body fat = 22.5 +/- 1.9%; means +/- SE) participated in this investigation. ", "The expression of OB-R protein was determined in skeletal muscle, subcutaneous adipose tissue, and hypothalamus using a polyclonal rabbit anti-human leptin receptor. ", "Three bands with a molecular mass close to 170, 128, and 98 kDa were identified by Western blot with the anti-OB-R antibody. ", "All three bands were identified in skeletal muscle: the 98-kDa and 170-kDa bands were detected in hypothalamus, and the 98-kDa and 128-kDa bands were detected in thigh subcutaneous adipose tissue. ", "The 128-kDa isoform was not detected in four subjects, whereas in the rest its occurrence was fully explained by the presence of intermuscular adipose tissue, as demonstrated using an anti-perilipin A antibody. ", "No relationship was observed between the basal concentration of leptin in serum and the 170-kDa band density. ", "In conclusion, a long isoform of the leptin receptor with a molecular mass close to 170 kDa is expressed at the protein level in human skeletal muscle. ", "The amount of 170-kDa protein appears to be independent of the basal concentration of leptin in serum." ]

{ "pile_set_name": "PubMed Abstracts" }

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[ "import os\nimport torch\nimport util.util as util\n\n\nclass BaseModel():\n def name(self):\n return self.__class__.__name__.lower()\n\n def initialize(self, opt):\n self.opt = opt\n self.gpu_ids = opt.gpu_ids\n self.isTrain = opt.isTrain\n self.", "Tensor = torch.cuda.", "FloatTensor if self.gpu_ids else torch.", "Tensor\n self.save_dir = os.path.join(opt.checkpoints_dir, opt.name)\n self._count = 0\n\n def set_input(self, input):\n self.input = input\n\n def forward(self):\n pass\n\n # used in test time, no backprop\n def test(self):\n pass\n\n def get_image_paths(self):\n pass\n\n def optimize_parameters(self):\n pass\n\n def get_current_visuals(self):\n return self.input\n\n def get_current_errors(self):\n return {}\n\n def save(self, label):\n pass\n\n def print_optimizer_param(self):\n # for optimizer in self.optimizers:\n # print(optimizer)\n print(self.optimizers[-1])\n\n def save(self, label=None):\n epoch = self.epoch\n iterations = self.iterations\n\n if label is None:\n model_name = os.path.join(self.save_dir, self.name() + '_%03d_%08d.pt' % ((epoch), (iterations)))\n else:\n model_name = os.path.join(self.save_dir, self.name() + '_' + label + '.pt')\n \n torch.save(self.state_dict(), model_name)\n\n def _init_optimizer(self, optimizers):\n self.optimizers = optimizers\n for optimizer in self.optimizers:\n util.set_opt_param(optimizer, 'initial_lr', self.opt.lr)\n util.set_opt_param(optimizer, 'weight_decay', self.opt.wd)\n" ]

{ "pile_set_name": "Github" }

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[ "Dear editor,\n\nAcute Kidney Injury (AKI) complicates a COVID-19 infection in up to 30% of the patients \\[[@bb0005], [@bb0010], [@bb0015], [@bb0020], [@bb0025], [@bb0030], [@bb0035]\\]. ", "The need for Renal Replacement Therapy (RRT) varied from 2 to 22% \\[[@bb0040], [@bb0045], [@bb0050], [@bb0055], [@bb0060]\\]. ", "Reported mortality rates for patients with RRT varies from 51.6--100% \\[[@bb0030], [@bb0035], [@bb0040],[@bb0065],[@bb0070]\\]. ", "These mortality rates might suggest that renal replacement therapy appears to be prognostically important, especially when resources are limited. ", "In addition, due to the thrombogenicity of the patients suffering from COVID-19, filter life may be shorter due to filter clotting \\[[@bb0075]\\]. ", "The aim of this study was to investigate the mortality-rate and renal recovery in patients with AKI due to COVID-19. ", "A secondary aim was to investigate the filter life times and the effect of different anticoagulants.", "\n\nAll patients admitted to the Intensive Care Unit (ICU) of the Rijnstate Hospital in Arnhem, The Netherlands from March 16th 2020 to May 10th 2020 were retrospectively studied. ", "Follow-up lasted until May 13th 2020. ", "Inclusion criterium was a positive COVID-19 Polymerase Chain Reaction (PCR). ", "Exclusion criterium was an admission shorter than 24 h. Ethical approval and requirement for written informed consent was not required due to the retrospective and non-interventional nature of the study.", "\n\nAll patients with COVID-19 were admitted to the ICU for respiratory failure. ", "All patients received thromboprophylaxis with daily nadroparin 2800 IE s.c., ", "which was increased to 5600 IE s.c. ", "daily following national guidelines on April 10th, 2020.When AKI occurred, post-renal and pre-renal causes were excluded. ", "CRRT was started on indication, such as hyperkaliemia, fluid overload unresponsive to diuretics and severe metabolic acidosis. ", "RRT was not an indication for ICU-admission, since a dialysis unit is available.", "\n\nIn our institution the primary method of RRT is Continuous VenoVenous Hemofiltration (CVVH) anticoagulated with citrate. ", "When patients receive systemic anticoagulation with heparin for another indication, a bicarbonate-buffered substitution fluid is chosen and heparin is targeted at an APTT of 50--70 s. A filter change is scheduled routinely after 72 h. Intermittent Hemodialysis (IHD) is the secondary modality.", "\n\nThe indication for RRT is evaluated with every filter change. ", "RRT is only restarted if clearance or diuresis, with diuretics if needed, is deemed insufficient by the treating physician.", "\n\nThe patients were categorized in a AKI-group, defined by a KDIGO-stage 1, 2 and 3 and a non-AKI-group. ", "The patients from the AKI-group were categorized in a RRT-group and a non-RRT-group. ", "All data are presented as median (interquartile range)\\[minimum-maximum\\]. ", "95% Confidence Interval (95%CI) was calculated for proportions. ", "The Mann-Whitney-*U* test was used to compare continuous data between groups, the Fisher\\'s exact test was used for categorical data. ", "A *p* \\< 0.05 was considered significant.", "\n\nA total of 39 patients were admitted to the ICU for COVID-19. ", "37 patients were included for analysis, of which 6 (16%) patients were still admitted to the ICU on May 13th.", "\n\nTwenty-two (60%, 95%CI: 42--75) patients developed AKI. ", "Hypertension, diabetes mellitus and chronic kidney disease were more frequent present in the AKI group, albeit not reaching significance. ", "The severity of illness was comparable between the AKI and non-AKI group, except for a higher level of creatinine in the AKI-group upon admission. ", "Mortality tended to be increased in the AKI-group (41%, 95%CI: 20--64) compared to the non-AKI-group (20%, 95%CI: 0--40). ", "Of the AKI-group patients, renal function recovered in 64% to a KDIGO-stage 1 upon discharge from ICU.", "\n\nThirteen of the 22 patients with AKI (59%, 95%CI, 36--79) were treated with RRT. ", "The patients in the RRT-group were younger, had higher levels of creatinine and BUN and oliguria was more frequently present compared to the non-RRT group. ", "RRT was initiated a median of 6 days (4--12)\\[2--19\\] after ICU admission and lasted for 7 days (4--9)\\[1--19\\]. ", "All patients received CVVH and five received at least one session of IHD. ", "The indication for starting RRT were acidosis (*n* = 4), hyperkaliemia (*n* = 7) and fluid overload (*n* = 2).", "\n\nComparable mortality rates were seen in the RRT (39%, 95%CI:14--68) versus non-RRT group (44%, 95%CI:14--79), *p* = 1.000. ", "Four patients that did not survive in the RRT-group needed RRT until death. ", "The KDIGO-stages on discharge were comparable between the groups. ", "None of the patients required RRT after ICU discharge.", "\n\nFifty-three filters were used for CVVH and filter lifetime was 27 h (14--63) \\[2--78\\], 35 (66%) of which were regional anticoagulated with citrate. ", "Thirty filters (57%) failed prematurely and the lifetime of these filters was 21 h (13−33)\\[4--71\\]. ", "No data were available regarding cause of failing. ", "No correlation was found between the filter lifetime and dose of LMWH as thromboprophylaxis (2800 IE: 25 h (18--61)\\[4--72\\] versus 5600 IE: 26 h (13--66)\\[5--72\\], *p* = 0.905), therapeutic or prophylactic anticoagulation (20 h (14--30)\\[7--48\\] versus 21 h (9--40)\\[4--71\\], *p* = 0.950) or citrate versus bicarbonate-buffered substitution fluid (21 h (13--27)\\[4--71\\] versus 21 h (12--40)\\[7--48\\], *p* = 0.801). ", "Prone position showed a non-significant lower filter lifetime than supine position (20 h (8--51)\\[2--72\\] versus 40 h (20--64)\\[6--78\\], *p* = 0.071).", "\n\nThe current study shows a mortality rate of 39% in patients with RRT for COVID-19 associated AKI, which strengthens the likelihood of a mortality around the lower limit of the reported 51.6--100% \\[[@bb0030], [@bb0035], [@bb0040],[@bb0065],[@bb0070]\\]. ", "Second, renal function recovered to KDIGO-stage 1 in 64% of the patients with AKI when discharged from the ICU. ", "This is merely a suggestion of renal recovery, since no long-term data are available. ", "One can conclude, however, that RRT is a temporary intervention and associated with similar short term mortality rates as patients with AKI without RRT.", "\n\nFurthermore, the low filter lifetimes were not associated with anticoagulation. ", "Other reasons for a reduced filter lifetime may be increased filter clogging due to inflammatory proteins, a late response to alarms by the nursing staff due to personal protection equipment requirements or the decreased catheter performance due to prone positioning.", "\n\nIn conclusion, the need for RRT for AKI in critically ill patients with COVID-19 was often temporary in our cohort and was not associated with an increased mortality rate compared to AKI without the need for RRT. ", "This could imply that no threshold for initiating RRT based on futility of treatment is warranted. ", "This study found no support for the use of higher levels of anticoagulation to prolong the low filter lifetime ([Table 1](#t0005){ref-type=\"table\"} ).Table 1Characteristics and outcomes of the groups non-AKI, RRT and non-RRT.Table 1Non-AKI (*n* = 15)RRT (*n* = 13)Non-RRT (*n* = 9)P^a^P\\#Patient characteristicsAge (years)68 (63−70)\\[42−81\\]64 (59−69)\\[42−73\\]71 (70−73)\\[60−76\\]0.7520.014Gender (%male)11 (73%)10 (77%)6 (67%)1.0000.655BMI (kg/m^2^)27 (26−28)\\[20−43\\]29 (26−31)\\[22−34\\]27 (26−29)\\[21−34\\]0.4000.393Comorbidities-*Hypertension*2 (13%)3 (23%)5 (56%)0.1530.187-*Diabetes Mellitus*1 (7%)2 (15%)1 (11%)0.6331.000-*Chronic Renal Failure*0 (0%)1 (8%)2 (22%)0.2570.544

Severity of illness on admissionSOFA-score6 (6−7) \\[3−11\\]8 (6−8) \\[3−11\\]7 (6−8) \\[3−9\\]0.1610.471P/F-ratio (kPa)14.4 (11.1−25.6)\\[6.8−34.3\\]16.0 (12.9−19.1)\\[7.7−28.9\\]11.0 (9.1−15)\\[8−18.5\\]0.5470.104PEEP (cmH2O)12 (10−12)\\[10−16\\]13 (10−16)\\[8−16\\]14 (12−17)\\[10−18\\]0.2630.343Creatinine (μmol/L)63 (45−75)\\[35−90\\]84 (74−92)\\[52−357\\]92 (65−98)\\[48−159\\]0.0020.845BUN (mmol/L)6.6 (4.2−7.8)\\[3.1−14.0\\]7.5 (6.5−10.3)\\[3.5−22.5\\]7 (5.7−12.1)\\[4.8−18.6\\]0.0920.948Mechanical ventilation14 (93%)13 (100%)8 (89%)1.0000.409

Severity of AKIKDIGO-stage AKI0 (0%)/ 0 (0%)/ 13 (100%)5 (56%)/ 3 (33%)/ 1 (11%)0.000Highest creatinine (μmol/L)390 (308−451)\\[178−500\\]125 (98−150)\\[93−338\\]0.000Highest BUN (mmol/L)42.1 (36.8−50.7)\\[17.6−66.2\\]22 (19.8−28.1)\\[9.1−30.8\\]0.004Oliguria (\\<500 ml/24 h)8 (62%)1 (11%)0.031Duration of RRT7 (4−9)\\[1−19\\]

OutcomesDuration of ICU admission (days) (*n* = 31)18 (9−27)\\[1−31\\]24 (14−33)\\[8−37\\]19 (7−37)\\[1−52\\]0.2580.762Mortality (n = 31)3 (20%)5 (39%)4 (44%)0.2571.000Still in ICU2 (13%)3 (23%)1(11%)1.0000.616KDIGO-stage at discharge (1/2/3)7 (54%)/ 2 (15%)/ 4 (31%)7 (78%)/ 0 (0%)/ 2 (22%)0.367RRT after discharge0 (0%)0 (0%)N/A[^1]\n\nEthics approval {#s0005}\n===============\n\nNot deemed necessary by the Dutch law.", "\n\nConsent to participate {#s0010}\n======================\n\nAll patients agreed on participation in retrospective studies in the study hospital.", "\n\nAvailability of data and material {#s0015}\n=================================\n\nAvailable upon reasonable request.", "\n\nDeclaration of Competing Interest\n=================================\n\nNone of the authors have any conflicts of interests.", "\n\n[^1]: \\^: Difference between the Non-AKI and the AKI-group (combined RRT and non-RRT group), \\#: difference between RRT and non-RRT group.", "\n" ]

{ "pile_set_name": "PubMed Central" }

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[ "---\nabstract: 'We present results of single-epoch very long baseline interferometry (VLBI) observations of gamma-ray bright active galactic nuclei (AGNs) using the Korean VLBI Network (KVN) at 22, 43, 86, and 129 GHz bands, which are part of a KVN key science program, Interferometric Monitoring of Gamma-ray Bright AGNs (iMOGABA). ", "We selected a total of 34 radio-loud AGNs of which 30 sources are gamma-ray bright AGNs with flux densities of $>6\\times10^{-10}$ ph cm$^{-2}$ s$^{-1}$. Single-epoch multi-frequency VLBI observations of the target sources were conducted during a 24-hr session on 2013 November 19 and 20. ", "All observed sources were detected and imaged at all frequency bands with or without a frequency phase transfer technique which enabled the imaging of 12 faint sources at 129 GHz, except for one source. ", "Many of the target sources are resolved on milliarcsecond scales, yielding a core-jet structure with the VLBI core dominating the synchrotron emission on the milliarcsecond scale. ", "CLEAN flux densities of the target sources are 0.43-28 Jy, 0.32-21 Jy, 0.18-11 Jy, and 0.35-8.0 Jy in the 22, 43, 86, and 129 GHz bands, respectively. ", "Spectra of the target sources become steeper at higher frequency with the mean of the spectral indices of -0.40, -0.62, and -1.00 in the 22-43 GHz, 43-86 GHz and 86-129 GHz bands, respectively, implying that the target sources become optically thin at higher frequency (e.g., 86-129GHz).'", "\nauthor:\n- 'Sang-Sung Lee, Kiyoaki Wajima, Juan-Carlos Algaba, Guang-Yao Zhao, Jeffrey A. Hodgson, Dae-Won Kim, Jongho Park, Jae-Young Kim, Atsushi Miyazaki, Do-Young Byun, Sincheol Kang, Jeong-Sook Kim, Soon-Wook Kim, Motoki Kino, and Sascha Trippe'\ntitle: 'Interferometric Monitoring of Gamma-ray Bright AGNs I: Results of Single-epoch Multifrequency Observations'\n---\n\nIntroduction\n============\n\nActive galactic nuclei (AGNs) are the most powerful and violent celestial objects in the Universe. ", "AGNs emit a wide range of electromagnetic radiation in the radio to gamma-ray range, producing huge luminosity ($\\sim10^{42}-10^{48}$ erg s$^{-1}$) in very compact emitting regions on sub-pc scales; their emission is often highly variable and polarized [see e.g., @kro99]. ", "The AGNs are believed to have supermassive black holes (SMBH) in the centers, accretion disks around the SMBHs, and relativistic jets launched perpendicular to the accretion disk plane into interstellar space. ", "Relativistic jets of the radio-loud AGNs often show variability in brightness (e.g., in radio, optical, etc.) ", "on timescales of hours to years, and morphological changes on milliarcsecond (mas) scale [see e.g., @boe+12 for review]. ", "Very rapid and strong variabilities (or flares) in the gamma-ray range from radio-loud AGNs have been observed during intensive gamma-ray monitoring of AGNs by several gamma-ray space telescopes: INTEGRAL [^1], AGILE [^2], FERMI [^3], etc. ", "The gamma-ray flares were detected from more than 100 AGNs including 3C 273, 4C +21.35, 4C 454.3 and 1510-089, by the Fermi Gamma-ray Space Telescope (GST) [see @kan+15 for references]. ", "To understand the gamma-ray flares in the AGNs, multiwavelength monitoring studies have been conducted to investigate the correlation between emission at gamma-ray and other wavelengths [e.g., @mar+08; @abd+10]. ", "The gamma-ray flares are correlated with the variability in brightness, polarization, and morphology of the jets at low energy regimes (e.g., radio, optical, etc.). ", "The correlation of the gamma-ray flares with multiwavelength variability, in principle, implies co-spatiality of the gamma-ray flaring regions and the emission regions at other wavelengths.", "\n\n[@mar+08] suggested that the gamma-ray flares from BL Lac may be generated through inverse Compton scattering in the innermost region of the jets threaded by a helical magnetic field or in a bright very long baseline interferometry (VLBI) core region corresponding to a standing shock wave, through compression by the shock front. [", "@abd+10] reported that the gamma-ray flares correlated with the change of optical polarization angle of 3C 279 provide evidence for the co-spatiality of the gamma-ray and optical emission regions with a highly ordered jet magnetic field in a curved trajectory within the jet. ", "The different understandings of the cause and location of the gamma-ray flares imply that either the gamma-ray flares are generated under various situations or our understanding of the gamma-ray flares may still be uncertain.", "\n\nGamma-ray flares leading a delayed outburst at radio frequencies [e.g., @jor+01] motivated the conducting of many single-dish and VLBI observations (or monitoring programs) at centimeter (cm) and millimeter (mm) wavelengths [@sav+02; @LV03; @lis+09; @ojh+09; @mar+11; @ang+12; @nag+13]. ", "Those VLBI monitoring programs are conducted only at a single frequency of $\\le$43 GHz, except for the TANAMI [@ojh+09] at 8.4 and 22 GHz, implying that those programs are not able to determine frequency-dependent properties of the gamma-ray flaring AGNs on mas-scales, including such properties as spectral index variation, time-dependent multiwavelength light curves of mas-scale structures, etc., ", "which may be very important to investigate the correlation of the gamma-ray flares with both the optically thin and thick emissions of the jets.", "\n\nThe Korean VLBI Network (KVN) has enabled us to regularly obtain mas-scale images of gamma-ray bright AGNs at cm-to-mm wavelengths, leading to a key science program (KSP) of the KVN, the Interferometric Monitoring of Gamma-ray Bright AGNs (iMOGABA), which is a VLBI monitoring program for about 30 gamma-ray bright AGNs using the KVN at multifrequency bands (22-129 GHz). ", "The iMOGABA initially started in 2012 December by conducting monthly one 24-hr VLBI observation in the 22, 43, 86, and 129 GHz bands. ", "The iMOGABA has been selected as a KVN KSP since 2015 March, aiming at studying the origins of the gamma-ray flares of the AGNs. ", "We selected a total of 34 radio-loud AGNs, as summarized in Table \\[t1\\], of which 30 sources are gamma-ray bright AGNs with their flux densities of $>6\\times10^{-10}$ ph cm$^{-2}$ s$^{-1}$, including 24 sources monitored by the Fermi Gamma-ray Space Telescope using the Large Area Telescope on board. ", "The selected sources consist of 24 quasars, 7 BL Lacs, and 3 radio galaxies.", "\n\nIn this paper, the first representative paper from the iMOGABA program, we report the results of a single-epoch VLBI observations of the iMOGABA. ", "In Section \\[obs\\_analysis\\], the observations and data analysis of the single-epoch VLBI session used in this paper is described. ", "Then, we present the results of the single-epoch observations in Section \\[results\\]; in Section \\[dis\\], we present our discussion. ", "Finally, in Section \\[sum\\], we summarize what we have found.", "\n\nObservations and data analysis\\[obs\\_analysis\\]\n===============================================\n\nObservations\\[obs\\]\n-------------------\n\nWe observed a total of 34 radio-loud AGNs in the 22 GHz, 43 GHz, 86 GHz, and 129 GHz bands on 2013 November 19 UT 02:00 - November 20 UT 01:53, using the KVN which consists of three identical 21-m radio telescopes [@lee+11]: KVN Yonsei (KY), KVN Ulsan (KU), and KVN Tamna (KT), with baseline lengths of 305–476 km [@lee+14], and a simultaneous multifrequency observing system [@han+08; @han+13]. ", "All sources were observed with 1-8 scans of 5 min in length. ", "The observing frequencies were 21.700–21.764 GHz, 43.400–43.464 GHz, 86.800–86.864 GHz, and 129.300–129.364 GHz, and in left circular polarization (LCP). ", "The ratio of the starting frequencies is an integer so that the frequency phase technique can be applied to faint sources [@alg+15]. ", "The total bandwidth is 256 MHz and is divided evenly for each frequency band. ", "In order to measure changes in the opacity of the atmosphere during the observations, we conducted sky tipping curve measurements every hour, i.e., we measured the system temperatures at 8 elevations: 18.21$^\\circ$, 20.17$^\\circ$, 22.62$^\\circ$, 25.77$^\\circ$, 30.00$^\\circ$, 36.03$^\\circ$, 45.58$^\\circ$, and 65.38$^\\circ$, during the observations. ", "Cross-scan observations for target sources were conducted every scan to correct antenna pointing offsets, which are the main source of amplitude uncertainty in KVN observations. ", "The received signals were digitized (i.e. 2-bit quantized) by digital samplers in the antenna cabin and transmitted through optical fibers to the observing building. ", "The transferred digital signals were requantized and divided into 16 sub-bands (IFs) of 16 MHz wide by a digital filter bank, and recorded by the Mark 5B system at a recording rate of 1024 Mbps. ", "Correlation of the data was performed with the DiFX software correlator in the Korea-Japan Correlator Center [@lee+15a].", "\n\nData analysis\\[da\\]\n-------------------\n\nThe DiFX correlator produced the spectrum of the cross-correlation function with resolution of 0.125 MHz and accumulation period of 1 s. Post-correlation processing was done using the NRAO Astronomical Image Processing System (AIPS). ", "A standard AIPS procedure was applied. ", "An antenna-based fringe fitting was conducted using AIPS task FRING. ", "KVN Ulsan (KU) was selected as the reference antenna. ", "The 5 min long scans were split into solution intervals that were 30 s long. ", "Baseline-based fringe solutions (phase delays and delay rates) were searched for individual IF at all frequency bands. ", "The baseline-based fringe solutions were used to determine the antenna-based fringe solutions.", "\n\nAll sources were detected at lower frequencies (e.g., 22-86 GHz) with this standard post-correlation processing. ", "However, about a dozen of the observed sources were not detected in the 129 GHz band. ", "In order to detect the non-detected sources, the FPT technique was applied, using an automatic VLBI data reduction pipeline developed for the KVN observations. ", "The operation of the KVN Pipeline was described in detail by [@hod+16]. ", "Thanks to the FPT technique, i.e., by transferring phase solutions from lower frequencies to higher as described by [@rio+11] and [@rio+14], sensitivity at high frequency was improved, and all of the non-detected sources were detected in the 129 GHz band.", "\n\nAmplitude calibrations were performed based on system temperatures measured during observations at each station and on elevation dependence of the antenna gains provided. ", "The system temperatures were corrected for the atmospheric opacity estimated from the sky tipping curve measurements conducted every hour. ", "We expect that thanks to the good quality of the system temperatures, antenna gains, and atmospheric opacity for KVN stations, the uncertainty of the amplitude calibration is witin 10-30% at 22-129 GHz bands. ", "Re-normalization of the fringe amplitudes was made to correct for the amplitude distortion due to quantization, and the quantization and re-quantization losses were corrected [@lee+15b].", "\n\nImaging with calibrated data\\[imaging\\]\n---------------------------------------\n\nThe phase- and amplitude-calibrated data were used to produce CLEAN contour maps of the sources via the Caltech DIFMAP software [@she+94]. ", "The calibrated data were averaged in frequency, and the data at band edges were chopped to avoid flux loss due to bandpass shape. ", "The [*uv*]{}-data were also averaged in time over 30 seconds in the 22, 43, and 86 GHz bands, and over 10 seconds in the 129 GHz band, taking into account coherence time at each frequency bands, and expecting a decoherence loss of upto 30% at 86-129GHz bands. ", "Some outliers in the $uv$-data were flagged by investigating the visibility amplitude.", "\n\nThe averaged and edited [*uv*]{}-data were then fitted using a single circular two-dimensional Gaussian model, and the visibility phase was self-calibrated with the model. ", "After removing the single Gaussian model, a combination of CLEAN point source models was applied. ", "The visibility phase was again self-calibrated with the CLEAN model to produce the final CLEAN contour maps of the detected sources, when available. ", "The visibility amplitude was not modified.", "\n\nThe residual noise in the final CLEAN map was investigated to evaluate the quality of the image, taking into account the assumption that the residual noise of the properly CLEAN image is random noise, and hence the amplitude of each pixel in the residual map should have a Gaussian distribution. ", "So, the noise in the final image can be expressed quantitatively by the ratio of image noise rms to its mathematical expectation, $\\xi_{\\rm r} = s_{\\rm r} / s_{\\rm {r,exp}}$, where $|s_{\\rm r}|$ is the maximum absolute flux density in the residual image and $|s_{\\rm r,exp}|$ is the expectation of $s_{\\rm r}$. For Gaussian noise with a zero mean, the expectation of $s_{\\rm r}$ is $|s_{\\rm {r,exp}}| = \\sigma_{\\rm r} { \\left[ \\sqrt{2} \\ln{\\left( \\frac{N_{\\rm pix}} {\\sqrt{2\\pi}\\sigma_{\\rm r}} \\right) }\\right]}^{1/2}$, where $N_{\\rm pix}$ is the total number of pixels in the image, and $\\sigma_{\\rm r}$ is the image noise rms. ", "If $ \\xi_{\\rm r} \\rightarrow 1 $, the residual noise approaches Gaussian noise; if $ \\xi_{\\rm r} > 1 $, not all the structure has been adequately recovered; if $ \\xi_{\\rm r} < 1 $, the image model has an excessively large number of degrees of freedom [@lob+06]. ", "The values of $\\xi_{\\rm r} $ of the images obtained in this paper are 0.42-0.74 at 22 GHz, 0.41-0.77 at 43 GHz, 0.43-0.75 at 86 GHz, and 0.43-0.81 at 129 GHz, as shown in Figure \\[fig-hist-q\\] and summarized in Table \\[t2\\], implying that the images adequately represent the structure detected in the visibility data.", "\n\nModel fitting and estimating parameters\\[modelfit\\]\n---------------------------------------------------\n\nCircular two-dimensional Gaussian models were used to fit the final CLEAN images, yielding the general fit parameters: [*$S_{\\rm tot}$*]{} (total flux density), [*$S_{\\rm peak}$*]{} (peak flux density), [*$\\sigma_{\\rm rms}$*]{} (post-fit rms), $d$ (size), $r$ (radial distance, for jet components), $\\theta$ (position angle, measured for jet components, with respect to the location of the core component), as summarized in Table \\[t3\\]. ", "The uncertainties of the fit parameters were estimated, based on the signal-to-noise ratio of each component detection, by adopting an analytical first order approximation given by [@fom99]: $\\sigma_{\\rm peak} = \\sigma_{\\rm rms}{\\left({1+\\frac{S_{\\rm peak}}{\\sigma_{\\rm rms}}}\\right)}^{1/2}$, $\\sigma_{\\rm tot} = \\sigma_{\\rm peak}{\\left({1+\\frac{S_{\\rm tot}^2}{S_{\\rm peak}^2}}\\right)}^{1/2}$, $\\sigma_{d} = d\\frac{\\sigma_{\\rm peak}}{S_{\\rm peak}}$, $\\sigma_{r} = \\frac{1}{2}\\sigma_{d}$, and $\\sigma_{\\theta} ={\\rm atan}\\left(\\frac{\\sigma_{r}}{r}\\right)$, where $\\sigma_{\\rm peak}$, $\\sigma_{\\rm tot}$, $\\sigma_{\\rm rms}$, $\\sigma_{d}$, $\\sigma_{r}$, and $\\sigma_{\\theta}$ are the uncertainties of peak flux density, total flux density, post-fit rms, size, radial distance, and position angle of a component, respectively. ", "A component was considered to be unresolved when the fitted component size $d$ is smaller than its minimum resolvable size [@lob05] as given by $d_{\\rm min}=\\frac{2^{1+\\beta/2}}{\\pi}{\\left[{\\pi ab\\ln2\\ln{\\frac{\\rm S/N}{{\\rm S/N}-1}}}\\right]}^{1/2}$, where [*a*]{} and [*b*]{} are the axes of the restoring beam, S/N is the signal-to-noise ratio, and $\\beta$ is the weighting function, which is 0 for natural weighting or 2 for uniform weighting. ", "If $d<d_{\\rm min}$, the uncertainties were estimated according to $d=d_{\\rm min}$.\n\nThe total flux density and measured size of a Gaussian component leads to a simple estimation of the rest frame brightness temperature $T_{\\rm b}$ of the given emission region represented by the Gaussian model as $T_{\\rm b} = \\frac{2\\ln{2}}{{\\pi}{k}}\\frac{S_{\\rm tot}\\lambda^2}{d^2}(1+z)$, where $\\lambda$ is the wavelength of observation, $z$ is the redshift, and $k$ is the Boltzmann constant. ", "If $d < d_{\\rm min}$, then the lower limit of $T_{\\rm b}$ is obtained using $d=d_{\\rm min}$.\n\nResults\\[results\\]\n==================\n\nOut of 34 sources, 32 sources were detected and imaged at all frequency bands with or without a frequency phase transfer technique that enabled us to detect and image 13 faint sources at 129 GHz, except for 0218+357 which was detected for only one baseline at all frequency bands. ", "The first 129 GHz VLBI images were made for most of the sources in this project.", "\n\nIn Figure \\[fig-image\\], CLEAN contour maps for each source are presented for the 22, 43, 86, and 129 GHz bands, when available. ", "A set of plots for each source at each frequency consists of a contour map in the left panel, a plot of the corresponding visibility amplitude against [*uv*]{}-radius in the top right panel, and a plot of the corresponding [*uv*]{}-sampling distribution in the bottom right panel. ", "The contour map is shown with the X- and Y-axes in units of mas. ", "The source name and the observing frequency are given at the top of the map. ", "The FWHM of the restoring beam is drawn as a shaded ellipse on the map. ", "The peak flux density and rms noise level are identified in the lower right corner of the map. ", "The contours are drawn with a logarithmic spacing at -1, 1, 1.4,...,$1.4^n$ of the lowest flux density level which corresponds to three times the rms noise level. ", "Most contour maps are centered on their brightest emission region (which is considered to be a VLBI core with fainter emission regions being the corresponding jet component, except for 3C 84 and 4C+39.25), but for some maps with extended source structure, the map center is shifted to fit the map in the box. ", "The plot of the visibility amplitude, at the top right of each set, is drawn as a function of the [*uv*]{}-radius, i.e., the length of the baseline used to obtain the corresponding visibility point in units of $10^6\\lambda$, where $\\lambda$ is the observing wavelength. ", "The visibility amplitude (i.e., the correlated flux density) is shown in units of Jy. ", "The [*uv*]{}-sampling distribution, at the bottom right of each set, shows the distribution of the visibility in the [*uv*]{}-plane, whose range corresponds to that of the [*uv*]{}-radius. ", "For the 12 sources (0235+164, 0528+134, 0735+178, 0827+243, 0836+710, 1127-145, 1156+295, 1222+216, 1343+451, 1611+343, and 3C 286) the FPTed images, i.e., the images obtained by the FPT technique, are presented for the 129 GHz band. ", "In particular, the 43 and 86 GHz images for 3C 286 are also FPTed.", "\n\nThe KVN observations for this paper were done without the phase-referencing technique, i.e., without relative (or absolute) astrometric information of core or jet components with respect to calibrators. ", "So, we considered a brightest emission region to be a VLBI core in each image and the others the jet, following a general strategy for identifying VLBI cores. ", "However, we found that for some cases, maybe rare but well-known, the brightest component may not be the core. ", "For example, 3C 84 (0316+413), the J3 component is brighter than the core (C) at 43 and 86 GHz. ", "At 43 GHz, in particular, the J3 component was centered and the core was located in the northern area in the beginning of the imaging process due to its brightness. ", "Considering the spectral index of the core (C) to be flat, we identified the northern component as a core, and shifted the map to south. ", "Another exceptional source is 4C $+$39.25 (0923+392). ", "The eastern component (J1) is brighter than the western component (C) and was located in the map center in the imaging process. ", "Since, however, the fainter component is usually identified as the core [e.g., @nii+14], we considered the fainter component as the core and shifted the map to have the core in the center.", "\n\nParameters of the contour maps presented in Figure \\[fig-image\\] are summarized in Table \\[t2\\]. ", "For each image, Table \\[t2\\] lists the source name, the observing frequency band, the parameters of the restoring beam (the size of the major axis $B_{\\rm maj}$, the minor axis $B_{\\rm min}$, and the position angle of the beam $B_{\\rm PA}$), the total flux $S_{\\rm KVN}$, the peak flux density $S_{\\rm p}$, the off-source RMS $\\sigma$, the dynamic range of the image $D$, and the quality $\\xi_{\\rm r}$ of the residual noise in the image.", "\n\nThe parameters of each model-fit component are listed in Table \\[t3\\]: the total flux $S_{\\rm tot}$, peak flux density $S_{\\rm peak}$, size $d$, radius, $r$ (only for jet components), position angle $\\theta$ (only for jet components), and measured brightness temperature $T_{\\rm b}$. In cases of multiple components (i.e., VLBI core and jet components) fitted, the parameters of the core component are followed by those of the jet components. ", "The estimated uncertainties are given as in Section \\[modelfit\\]. ", "The upper limits of size $d$, and the lower limits of brightness temperature $T_{\\rm b}$ are in italics with flag symbols.", "\n\nDiscussion\\[dis\\]\n=================\n\nSource morphology on mas scales\n-------------------------------\n\nMany of the target sources are resolved on mas scales, yielding a core-jet structure. ", "Out of 33 sources imaged, 22 sources show a core-jet structure at at least one of the observing frequency bands. ", "Most of the sources with core-jet structure are imaged to show a single jet component, except for 0316+413 (3C 84), 1226+023 (3C 273B), 1611+343, 1641+399 (3C 345), 2230+114 (CTA102), and 2251+158 (3C 454.3), which show more than one jet component at at least one frequency band on the scales of 1-11 mas, contributing to the CLEAN flux density of the sources by $<$50%, as summarized in Table \\[t3\\]. ", "Although many of the target sources are resolved, they are highly core-dominated in flux, i.e., the VLBI core flux density ($S_{\\rm c}$) dominates the synchrotron emission on the mas-scales ($S_{\\rm KVN}$), as shown in Figure \\[fig-hist-ratio\\]. ", "Some of the very compact sources show a ratio of $S_{\\rm c}/S_{\\rm KVN}$ larger than unity due to uncertainty of the CLEAN flux and of the model fitting.", "\n\nThe distributions of angular size for the core components of the imaged sources were investigated. ", "As introduced in Section \\[modelfit\\], a core component was considered to be unresolved when the fitted core size was smaller than its minimum resolvable size, yielding the upper limit of the angular size. ", "The numbers of unresolved cores are 14 (22 GHz), 3 (43 GHz), 4 (86 GHz), and 5 (129 GHz) out of 33 imaged sources. ", "Excluding the upper limits, the mean (and median) values of the measured core angular sizes are 1.135 mas (0.912 mas), 0.586 mas (0.591 mas), 0.411 mas (0.438 mas), and 0.232 mas (0.179 mas) in the 22, 43, 86, and 129 GHz bands, respectively, implying that the resolved core sizes become smaller at higher frequencies.", "\n\nBrightness temperature {#tb}\n----------------------\n\nFigure \\[fig-hist-tb\\] shows the brightness temperatures of the VLBI cores, including the lower limits (in grey), which were obtained for the unresolved cores (see Section \\[modelfit\\]). ", "Excluding the limits, the measured brightness temperatures are in the ranges of $2.1\\times10^{7}$ K - $7.5\\times10^{8}$ K, $2.1\\times10^{7}$ K - $3.8\\times10^{10}$ K, $1.4\\times10^{8}$ K - $3.2\\times10^{10}$ K, and $7.7\\times10^{8}$ K - $1.2\\times10^{11}$ K, at 22, 43, 86, and 129 GHz, respectively. ", "The mean values of the measured brightness temperature are $1.7\\times10^{9}$ K, $4.2\\times10^{9}$ K, $6.0\\times10^{9}$ K, and $1.7\\times10^{10}$ K in the 22, 43, 86, and 129 GHz bands, respectively, implying that the brightness temperatures of the sources become higher at higher frequency.", "\n\nThese results are different from those reported by [@lee13], [@lee14], and [@lee+16]: the brightness temperatures of the VLBI cores imaged at 86 GHz with the Global Millimeter VLBI Array (GMVA) are lower than those obtained at 2-15 GHz with the global VLBI array. ", "The mean values of the brightness temperatures for the VLBI cores in [@lee+16] are $8.9\\times10^{11}$ K and $1.3\\times10^{11}$ K at 15 and 86 GHz, respectively; these values are higher than those we obtained in this work, by factors of about 50 and 20, respectively, although the source samples and their sizes are different from each other. ", "This difference may be due to the spatial resolution difference between the global VLBI arrays, which have a maximum baseline of about 10000 km, and the KVN, with its maximum baseline of about 500 km. ", "However, the lower brightness temperatures at lower frequencies (e.g., 22 GHz) obtained with the KVN cannot be fully explained by the resolution difference. ", "One explanation may be that the sources resolved at 22 GHz with the KVN are largely different from those resolved with the global array, since half of the cores in our sample were unresolved. ", "Another explanation may be that the brightness temperature measurements at lower frequencies are affected partly by an instrumental beam blending effect: the core region may be diluted by jet emission [see e.g., @lee+16 and references therein]. ", "The core blending effect would make larger both the observed core flux density and the size. ", "In this case of the 22 GHz observations with the KVN, the increasing factor of the observed core size $d$ is much larger than that of the observed core flux density $S_{\\rm tot}$, and hence the brightness temperature ($\\propto S_{\\rm tot}/d^2$) becomes lower than its true value.", "\n\nSource spectra\n--------------\n\nThe 129 GHz images presented in this paper are the first results for most of the radio loud AGNs in our sample. ", "Moreover, the simultaneous multifrequency images obtained at four frequency bands (22-129 GHz) are also the first results for the radio-loud AGNs, enabling us to investigate mas-scale spectral information for the radio loud AGNs free from any variability of source. ", "Here we discuss the spectral properties of the target sources, taking into account the CLEAN flux densities obtained on mas-scales.", "\n\nThe CLEAN flux densities $S_{\\rm KVN}$ of the target sources obtained with the KVN are in the ranges of 0.43-28 Jy, 0.32-21 Jy, 0.18-11 Jy, and 0.35-8.0 Jy in the 22, 43, 86, and 129 GHz bands, respectively, as shown in Figure \\[fig-hist-CLEAN\\]. ", "The distributions of the CLEAN flux density peak at around 2 Jy (22 and 43 GHz bands) and 1 Jy (86 and 129 GHz bands); these values show that most of the sources are brighter than 0.1 Jy at all frequencies. ", "The mean values of the CLEAN flux density are 4.7 Jy (21.7 GHz), 3.8 Jy (43.4 GHz), 2.5 Jy (86.8 GHz), and 1.6 Jy (129.3 GHz), implying that the sources become fainter at higher frequency on mas-scales.", "\n\nTo investigate the spectral properties of the target sources, three models were used to fit it to the CLEAN flux density data: the power law, the broken power law, and the curved power law, as given by $$\\label{eqn:plaw}\nS=a \\nu^{\\alpha},$$ where $S$ is the CLEAN flux density in Jansky, $\\nu$ is the observing frequency in GHz, $a$ is constant in Jansky, and $\\alpha$ is the spectral index for the power law, $$\\label{eqn:blaw}\nS=b \\left\\{\\left(\\frac{\\nu}{\\nu_{\\rm c}}\\right)^{-\\alpha_{\\rm L}n}+\\left(\\frac{\\nu}{\\nu_{\\rm c}}\\right)^{-\\alpha_{\\rm H}n}\\right\\}^{-1/n},$$ where $b$ is constant in Jansky, $\\nu_{\\rm c}$ is a break frequency of the broken power law, $\\alpha_{\\rm L}$ and $\\alpha_{\\rm H}$ are the spectral indices at lower and higher frequencies than the break frequency, and $n$ is a numerical factor governing the sharpness of the break, here fixed to be 100 in order to make the break very sharp; and, $$\\label{eqn:claw}\nS=c_1 \\left(\\frac{\\nu}{\\nu_{\\rm r}}\\right)^{\\alpha +c_2 {\\rm ln}(\\nu/\\nu_{\\rm r})},$$ where $c_1$ (in Jansky) and $c_2$ are constant, $\\nu_{\\rm r}$ is a reference frequency, and $\\alpha$ is the spectral index at $\\nu_{\\rm r}$. As a first step, we attempt to fit the power law to the data. ", "When the power law does not fit to the data, we use the curved power law. ", "For 7 sources, the power law and curved power law do not fit well to the data and, hence, a broken power law is used to fit to the data for those sources. ", "The CLEAN flux spectra of the 32 sources (except for 3C 286) are shown in Figure \\[fig-spind\\] with their best fitting model and the best fitting parameters: the spectral index $\\alpha$ for the power law, the cut-off (turnover) frequency $\\nu_{\\rm c}$, the spectral indices at lower ($\\alpha_{\\rm L}$) and higher ($\\alpha_{\\rm H}$) frequencies than the break frequency, obtained from the broken power law, the cut-off (turnover) frequency $\\nu_{\\rm c}$, the peak flux density $S_{\\rm m}$, and the spectral indices between 22-43 GHz (KQ), 43-86 GHz (QW), and 86-129 GHz (WD), obtained from the curved power law. ", "Out of 32 sources, only 5 sources show the spectra well fitted with the power law; 27 sources have spectra with either a break or a curvature. ", "For the 32 spectra shown in Figure \\[fig-spind\\], we used the best fitting model to obtain spectral indices in the KQ-band, QW-band, and WD-band. ", "Figure \\[fig-hist-spind\\] shows the distributions of the spectral indices, with mean (median) values of -0.40 (-0.42), -0.62 (-0.66), and -1.00 (-0.99) in the KQ, QW, and WD bands, respectively, indicating that many sources become optically thin at higher frequency (e.g., in the 86 and 129 GHz bands).", "\n\nVLBI core size and jet geometry\n-------------------------------\n\nIn the VLBI observations, the location of the $\\tau=1$ surface of the AGN thick core depends on the frequency according to the relation $r\\propto\\nu^{-1/k_r}$, leading to the well-known ‘core-shift’ effect [see, e.g. @lob98; @hir05; @OG09; @alg+12]. ", "This implies that, at various observing frequencies, the VLBI core actually probes different distances from the SMBH. ", "At the same time, if we consider the VLBI core as the innermost upstream regions of the unresolved jet, this suggests that measuring the core size at different frequencies can help us to investigate the innermost jet size at different locations, via the core-shift and, hence, the jet’s geometry. ", "This approach has already been successfully applied in, for example, [@had+11] and [@alg+16]. ", "However, the former considered only one source, and the latter considered observations spanning over several years. ", "The iMOGABA does not have any of these drawbacks and can consider a whole sample of simultaneous multi-frequency observations.", "\n\nIn Figure \\[fig-geometry\\] we show a representative subset of sources to which this method has been applied. ", "Here we plot the core radius (1/2 of the size) against the inverse of the frequency, which is proportional to the distance from the SMBH. ", "We performed an exponential fit following $(size)\\propto(distance^{\\epsilon})$ to find the inferred jet geometry ($\\epsilon=1$ conical; $\\epsilon=1/2$ parabolic; c.f. [", "@ghi+85]). ", "In general, we can distinguish three different trends: i) all points seem to be reasonably well aligned and fit to a jet size increasing with distance (left column), ii) a certain convex trend is found for the data (middle column) or iii) other peculiar patterns are found (right column). ", "In the following we briefly discuss these cases.", "\n\nThere are several cases in which the data are well fitted by an exponential function, in agreement with the discussion above. ", "The largest group, however, shows an increase of the core size, which does not follow the expected exponential trend, but rather seems to show a size saturation threshold at lower frequencies. ", "One possibility is that, due to the large scatter and limited data in the [*uv*]{}-plane, a small offset in the amplitude in one scan may cause the fitted Gaussian size to be slightly different, especially in the case of compact sources, which are common in the iMOGABA sample.", "\n\nIn some cases, the fit indicates a jet with a size that roughly constant or decreasing with size; the jet may even show a possibly oscillatory pattern. ", "Whilst this phenomenology could be true for a reduced number of sources in very specific conditions for a given time, we believe that this is not the case here. ", "Instead, we suggest that this behavior is rather due to other effects such as jet blending, the existence of various unresolved components, or extremely large viewing angles. ", "As for the case mentioned above, the lack of a significant amount of data in the [*uv*]{}-plane may also contribute to a certain extent to the misidentification of some core sizes; thus, care should be taken. ", "Averaging of the data through various epochs may partially solve this issue. ", "This will be discussed in a forthcoming paper. ", "Further discussion can also be found in [@alg+16].", "\n\nSummary\\[sum\\]\n==============\n\nAn interferometric monitoring program for gamma-ray bright AGNs was launched and, by conducting monthly multifrequency VLBI observations of a total of 34 radio loud AGNs, continues to aim at revealing the origins of gamma-ray flares often detected in AGNs. ", "One of the observing sessions in the program was conducted in 2013 on November 19 and 20, yielding 32 sources detected and imaged at all frequency bands with or without use of frequency phase transfer technique. ", "The first 129 GHz VLBI images were made from most of the sources, establishing a 129 GHz VLBI image database with a size of 32 sources. ", "In addition to the CLEAN images, we used two-dimensional circular Gaussian models to fit the CLEAN images and obtained the VLBI core sizes and brightness temperatures.", "\n\nWe find that the 22 sources show the core-jet structure at at least one of the observing frequency bands. ", "Most of the sources with the core-jet structure are imaged to show a single jet component, except for six sources with multiple jet components on the scales of 1-11 mas, contributing to the CLEAN flux density of the sources by $<$50%. ", "Although many of the target sources are resolved, they are highly core-dominated in flux. ", "We also find that the resolved core sizes become smaller at higher frequencies, with the mean values of the measured core angular sizes of 1.135 mas, 0.586 mas, 0.411 mas, and 0.232 mas in the 22, 43, 86, and 129 GHz bands, respectively.", "\n\nThe mean values of the measured brightness temperature are $1.7\\times10^{9}$ K, $4.2\\times10^{9}$ K, $6.0\\times10^{9}$ K, and $1.7\\times10^{10}$ K in the 22, 43, 86, and 129 GHz bands, respectively, implying that the brightness temperatures of the sources become higher at higher frequency. ", "We find that these brightness temperatures are lower than those obtained with global VLBI arrays, indicating that the brightness temperature measurements are affected by the low spatial resolution of the KVN observations and by the instrumental beam blending effect, especially in the 22 GHz band.", "\n\nThanks to the simultaneous multifrequency VLBI observations, we are able to investigate the spectral properties free from any source variability. ", "We find that the sources become fainter at higher frequency, yielding optically thin spectra at mm wavelengths. ", "More sophisticated modelling studies for spectral energy distribution with data in broader wavelength bands will be presented in forthcoming papers on individual sources in the iMOGABA program.", "\n\nWe would like to thank the anonymous referee for important comments and suggestions which have enormously improved the manuscript. ", "We are grateful to all staff members at KVN who helped to operate the array and to correlate the data. ", "The KVN is a facility operated by the Korea Astronomy and Space Science Institute. ", "The KVN operations are supported by KREONET (Korea Research Environment Open NETwork) which is managed and operated by KISTI (Korea Institute of Science and Technology Information). ", "This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP) (No. ", "NRF-2016R1C1B2006697). ", "Dae-Won Kim and Sascha Trippe acknowledge support from the National Research Foundation of Korea (NRF) via grant NRF-2015-R1D1A1A-01056807. ", "Jongho Park acknowledges support via NRF PhD fellowship grant 2014H1A2A1018695. ", "Guang-Yao Zhao acknowledges the support from Korea Research Fellowship Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Science, ICT and Future Planning (NRF-2015H1D3A1066561).", "\n\n[*Facilities:*]{}\n\nAbdo, A. A., Ackermann, M., Ajello, M., et al. ", "2010, , 463, 919\n\nAlgaba, J.-C., Gabuzda, D. C., & Smith, P. S. 2012, , 420, 542\n\nAlgaba, J.-C., Zhao, G.-Y., Lee, S.-S., et al. ", "2015, JKAS, 48, 237\n\nAlgaba, J.-C., Nakamura, M., Asada, K., & Lee, S.-S. 2016, in prep.", "\n\nAngelakis, E., Fuhrmann, L., Nestoras, I., et al. ", "2012, J. Phys. ", "Conf. ", "Ser., ", "372, 012007\n\nBoettcher, M., Harris, D. 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", "2014, , 148, 84\n\nShepherd, M. C., Pearson, T. J., & Taylor, G. B. 1994, , 26, 987\n\nV[é]{}ron-Cetty, M.-P., & V[é]{}ron, P. 2006, , 455, 773\n\n[lcccccc]{} 0218$+$357 & & Q & 0.944 & 02 21 05.468 & $+$35 56 13.73456 & 4.6e-09\\\n0234$+$285 & 4C +28.07& Q & 1.206 & 02 37 52.405 & $+$28 48 08.98998 & 9.7e-09\\\n0235$+$164 & & B & 0.940 & 02 38 38.930 & $+$16 36 59.27450 & 1.0e-08\\\n0316$+$413 & 3C 84& G & 0.018 & 03 19 48.160 & $+$41 30 42.10558 & 2.1e-08\\\n0415$+$379 & 3C 111& G & 0.049 & 04 18 21.277 & $+$38 01 35.80018 & ...\\\n0420$-$014 & & Q & 0.916 & 04 23 15.800 & $-$01 20 33.06558 & 5.6e-09\\\n0528$+$134 & & Q & 2.070 & 05 30 56.416 & $+$13 31 55.14944 & 3.7e-09\\\n0716$+$714 & & B & 0.127 & 07 21 53.448 & $+$71 20 36.36340 & 2.2e-08\\\n0727$-$115 & & Q & 1.591 & 07 30 19.112 & $-$11 41 12.60064 & 1.8e-08\\\n0735$+$178 & & B & 0.450 & 07 38 07.393 & $+$17 42 18.99811 & ...\\\n0827$+$243 & & Q & 0.942 & 08 30 52.086 & $+$24 10 59.82027 & 1.1e-09\\\n0836$+$710 & & Q & 2.218 & 08 41 24.365 & $+$70 53 42.17302 & 1.3e-09\\\n0851$+$202 & OJ 287& B & 0.306 & 08 54 48.874 & $+$20 06 30.64077 & 5.9e-09\\\n0923$+$392 & 4C +39.25& Q & 0.695 & 09 27 03.013 & $+$39 02 20.85177 & ...\\\n1055$+$018 & & Q & 0.888 & 10 58 29.605 & $+$01 33 58.82359 & 6.5e-09\\\n1101$+$384 & Mrk 421& B & 0.031 & 11 04 27.313 & $+$38 12 31.79895 & 3.0e-08\\\n1127$-$145 & & Q & 1.184 & 11 30 07.052 & $-$14 49 27.38835 & 9.0e-10\\\n1156$+$295 & & Q & 0.725 & 11 59 31.833 & $+$29 14 43.82678 & 8.4e-09\\\n1222$+$216 & & Q & 0.434 & 12 24 54.458 & $+$21 22 46.38856 & 2.6e-08\\\n1226$+$023 & 3C 273B& Q & 0.158 & 12 29 06.699 & $+$02 03 08.59796 & 9.4e-09\\\n1228$+$126 & M87& G & 0.004 & 12 30 49.423 & $+$12 23 28.04365 & 1.3e-09\\\n1253$-$055 & 3C 279& Q & 0.536 & 12 56 11.166 & $-$05 47 21.52490 & 2.1e-08\\\n1308$+$326 & & Q & 0.997 & 13 10 28.663 & $+$32 20 43.78277 & 3.7e-09\\\n1328$+$307 & 3C 286& Q & 0.846 & 13 31 08.288 & $+$30 30 32.95924 & ...\\\n1343$+$451 & & Q & 2.534 & 13 45 33.172 & $+$44 52 59.57257 & 6.5e-09\\\n1611$+$343 & & Q & 1.400 & 16 13 41.064 & $+$34 12 47.90878 & 6.5e-10\\\n1633$+$382 & 4C +38.41& Q & 1.813 & 16 35 15.492 & $+$38 08 04.50043 & 1.1e-08\\\n1641$+$399 & 3C 345& Q & 0.593 & 16 42 58.809 & $+$39 48 36.99385 & 2.5e-09\\\n1749$+$096 & & B & 0.322 & 17 51 32.818 & $+$09 39 00.72829 & 4.3e-09\\\n1921$-$293 & & Q & 0.353 & 19 24 51.055 & $-$29 14 30.12115 & 2.2e-09\\\n2200$+$420 & & B & 0.069 & 22 02 43.291 & $+$42 16 39.97986 & 1.6e-08\\\n2223$-$052 & 3C 446& Q & 1.404 & 22 25 47.259 & $-$04 57 01.39090 & 1.9e-09\\\n2230$+$114 & CTA 102& Q & 1.037 & 22 32 36.408 & $+$11 43 50.90394 & 5.0e-09\\\n2251$+$158 & 3C 454.3& Q & 0.859 & 22 53 57.747 & $+$16 08 53.56073 & 1.1e-07\\\n\n[lcccrrrrrr]{} 0234$+$285 &K & 5.533 & 3.076 & 83.8 & 2.957 & 2.824 & 11 & 260 & 0.68\\\n&Q & 2.906 & 1.463 & 81.8 & 2.262 & 2.076 & 11 & 195 & 0.65\\\n&W & 1.459 & 0.723 & 82.9 & 1.384 & 1.234 & 35 & 35 & 0.70\\\n&D & 0.959 & 0.535 & $-$86.1 & 0.808 & 0.784 & 38 & 21 & 0.63\\\n0235$+$164 &K & 7.635 & 3.025 & $-$57.2 & 0.862 & 0.857 & 12 & 72 & 0.54\\\n&Q & 3.833 & 1.458 & $-$60.0 & 0.775 & 0.755 & 17 & 44 & 0.62\\\n&W & 1.887 & 0.701 & $-$60.4 & 0.432 & 0.420 & 54 & 8 & 0.49\\\n&D & 1.495 & 0.509 & $-$53.4 & 0.290 & 0.275 & 46 & 6 & 0.50\\\n0316$+$413 &K & 5.866 & 2.790 & 88.3 & 27.795 & 23.617 & 162 & 146 & 0.62\\\n&Q & 3.075 & 1.420 & $-$82.3 & 17.830 & 11.196 & 56 & 201 & 0.77\\\n&W & 1.446 & 0.688 & 80.9 & 10.350 & 4.951 & 67 & 73 & 0.71\\\n&D & 0.939 & 0.517 & $-$83.5 & 6.720 & 3.250 & 19 & 174 & 0.72\\\n0415$+$379 &K & 6.363 & 3.020 & 72.0 & 4.204 & 3.953 & 24 & 163 & 0.61\\\n&Q & 3.379 & 1.435 & 69.7 & 3.714 & 3.708 & 24 & 152 & 0.69\\\n&W & 1.710 & 0.712 & 69.7 & 3.830 & 3.724 & 30 & 124 & 0.59\\\n&D & 1.096 & 0.498 & 76.8 & 2.706 & 2.688 & 36 & 75 & 0.52\\\n0420$-$014 &K & 6.414 & 3.265 & $-$63.3 & 4.984 & 5.058 & 81 & 62 & 0.52\\\n&Q & 3.297 & 1.604 & $-$65.1 & 3.814 & 3.777 & 50 & 76 & 0.46\\\n&W & 1.664 & 0.800 & $-$66.3 & 2.452 & 2.453 & 17 & 144 & 0.46\\\n&D & 1.085 & 0.553 & $-$52.2 & 1.610 & 1.616 & 56 & 29 & 0.44\\\n0528$+$134 &K & 5.360 & 3.323 & 86.2 & 1.259 & 1.159 & 6 & 199 & 0.53\\\n&Q & 2.767 & 1.566 & 82.3 & 0.887 & 0.878 & 11 & 82 & 0.55\\\n&W & 1.344 & 0.776 & 86.7 & 0.532 & 0.519 & 19 & 27 & 0.56\\\n&D & 0.888 & 0.566 & $-$81.5 & 0.337 & 0.335 & 18 & 19 & 0.55\\\n0716$+$714 &K & 5.826 & 4.243 & $-$61.5 & 2.507 & 2.511 & 17 & 145 & 0.58\\\n&Q & 2.897 & 1.992 & $-$69.9 & 2.658 & 2.654 & 21 & 127 & 0.61\\\n&W & 1.462 & 0.975 & $-$70.8 & 2.064 & 2.045 & 31 & 66 & 0.58\\\n&D & 0.970 & 0.681 & $-$60.8 & 1.431 & 1.424 & 20 & 73 & 0.61\\\n0727$-$115 &K & 6.929 & 3.570 & $-$54.7 & 3.821 & 3.754 & 23 & 166 & 0.48\\\n&Q & 3.589 & 1.749 & $-$58.2 & 2.298 & 2.291 & 13 & 176 & 0.44\\\n&W & 1.757 & 0.888 & $-$57.4 & 1.155 & 1.155 & 12 & 95 & 0.43\\\n&D & 1.206 & 0.588 & $-$45.9 & 0.770 & 0.766 & 5 & 158 & 0.48\\\n0735$+$178 &K & 7.012 & 3.033 & $-$59.8 & 1.088 & 1.013 & 4 & 250 & 0.62\\\n&Q & 3.521 & 1.456 & $-$62.7 & 0.891 & 0.836 & 7 & 127 & 0.60\\\n&W & 1.867 & 0.708 & $-$61.1 & 0.687 & 0.569 & 18 & 31 & 0.59\\\n&D & 1.050 & 0.501 & $-$57.3 & 0.392 & 0.366 & 14 & 27 & 0.48\\\n0827$+$243 &K & 9.665 & 3.073 & 60.9 & 0.872 & 0.868 & 19 & 46 & 0.46\\\n&Q & 5.178 & 1.436 & 60.8 & 0.606 & 0.592 & 20 & 29 & 0.48\\\n&W & 2.603 & 0.713 & 61.2 & 0.305 & 0.273 & 7 & 38 & 0.47\\\n&D & 1.614 & 0.521 & 64.0 & 0.278 & 0.275 & 18 & 15 & 0.47\\\n0836$+$710 &K & 5.680 & 4.162 & $-$53.6 & 1.762 & 1.648 & 11 & 148 & 0.55\\\n&Q & 2.924 & 1.998 & $-$52.8 & 1.187 & 1.048 & 4 & 264 & 0.64\\\n&W & 1.466 & 0.991 & $-$53.7 & 0.688 & 0.601 & 16 & 38 & 0.55\\\n&D & 0.926 & 0.700 & $-$50.8 & 0.403 & 0.336 & 10 & 33 & 0.58\\\n0851$+$202 &K & 6.126 & 3.080 & $-$65.4 & 4.974 & 4.746 & 15 & 317 & 0.74\\\n&Q & 3.223 & 1.480 & $-$66.3 & 3.716 & 3.683 & 25 & 149 & 0.64\\\n&W & 1.585 & 0.734 & $-$64.7 & 2.425 & 2.453 & 48 & 51 & 0.70\\\n&D & 1.067 & 0.512 & $-$58.5 & 1.692 & 1.651 & 47 & 35 & 0.59\\\n0923$+$392 &K & 6.429 & 3.181 & $-$61.0 & 8.338 & 8.039 & 50 & 162 & 0.65\\\n&Q & 3.314 & 1.515 & $-$60.1 & 5.475 & 4.830 & 33 & 147 & 0.62\\\n&W & 1.697 & 0.730 & $-$63.0 & 3.173 & 2.376 & 49 & 48 & 0.59\\\n&D & 1.023 & 0.569 & $-$58.8 & 1.588 & 1.193 & 41 & 29 & 0.67\\\n1055$+$018 &K & 5.620 & 3.449 & $-$68.7 & 2.879 & 2.862 & 23 & 123 & 0.53\\\n&Q & 3.807 & 1.617 & $-$58.0 & 2.314 & 2.348 & 40 & 58 & 0.48\\\n&W & 1.754 & 0.781 & $-$60.4 & 1.607 & 1.484 & 28 & 53 & 0.57\\\n&D & 1.546 & 0.510 & $-$50.7 & 1.053 & 1.047 & 33 & 32 & 0.47\\\n1101$+$384 &K & 5.229 & 3.170 & $-$80.4 & 0.433 & 0.435 & 3 & 143 & 0.51\\\n&Q & 2.663 & 1.508 & $-$83.3 & 0.316 & 0.311 & 7 & 43 & 0.56\\\n&W & 1.329 & 0.741 & $-$82.8 & 0.222 & 0.191 & 9 & 20 & 0.54\\\n&D & 0.992 & 0.509 & 89.8 & 0.354 & 0.348 & 17 & 21 & 0.45\\\n1127$-$145 &K & 9.106 & 3.832 & 44.7 & 2.040 & 2.068 & 60 & 34 & 0.42\\\n&Q & 4.378 & 1.913 & 49.2 & 1.798 & 1.795 & 123 & 15 & 0.49\\\n&W & 2.228 & 0.933 & 51.9 & 1.496 & 1.404 & 76 & 19 & 0.52\\\n&D & 1.359 & 0.683 & 52.7 & 0.754 & 0.748 & 93 & 8 & 0.49\\\n1156$+$295 &K & 6.153 & 2.993 & 77.5 & 0.858 & 0.853 & 20 & 44 & 0.43\\\n&Q & 3.218 & 1.437 & 75.3 & 0.800 & 0.809 & 20 & 40 & 0.41\\\n&W & 1.656 & 0.702 & 75.3 & 0.672 & 0.635 & 24 & 26 & 0.48\\\n&D & 1.089 & 0.480 & 80.5 & 0.478 & 0.481 & 23 & 21 & 0.46\\\n1222$+$216 &K & 5.343 & 3.317 & $-$75.0 & 2.298 & 2.286 & 21 & 107 & 0.57\\\n&Q & 2.728 & 1.553 & $-$75.3 & 1.744 & 1.503 & 26 & 59 & 0.59\\\n&W & 1.399 & 0.760 & $-$73.3 & 1.086 & 0.778 & 11 & 68 & 0.61\\\n&D & 1.336 & 0.506 & $-$53.7 & 0.569 & 0.432 & 12 & 36 & 0.43\\\n1226$+$023 &K & 5.816 & 3.493 & $-$72.7 & 8.297 & 6.496 & 87 & 74 & 0.68\\\n&Q & 3.130 & 1.708 & $-$73.2 & 6.802 & 4.606 & 25 & 187 & 0.72\\\n&W & 1.604 & 0.801 & $-$66.0 & 3.688 & 2.219 & 47 & 47 & 0.69\\\n&D & 0.963 & 0.596 & $-$67.6 & 2.354 & 1.564 & 26 & 61 & 0.71\\\n1228$+$126 &K & 5.186 & 3.445 & $-$83.9 & 2.052 & 1.854 & 14 & 129 & 0.60\\\n&Q & 2.661 & 1.642 & $-$80.9 & 1.383 & 1.293 & 8 & 158 & 0.57\\\n&W & 1.353 & 0.793 & $-$78.8 & 0.956 & 0.947 & 14 & 70 & 0.66\\\n&D & 0.962 & 0.561 & $-$65.4 & 0.663 & 0.659 & 16 & 40 & 0.54\\\n1253$-$055 &K & 5.499 & 4.506 & 66.6 & 27.655 & 26.394 & 130 & 202 & 0.53\\\n&Q & 2.659 & 2.116 & $-$74.7 & 20.980 & 18.749 & 95 & 197 & 0.54\\\n&W & 1.885 & 0.777 & $-$66.9 & 12.517 & 7.642 & 26 & 298 & 0.64\\\n&D & 1.141 & 0.551 & $-$54.4 & 7.983 & 4.399 & 29 & 154 & 0.81\\\n1308$+$326 &K & 6.875 & 3.004 & 70.0 & 1.464 & 1.464 & 10 & 140 & 0.45\\\n&Q & 3.685 & 1.411 & 69.1 & 1.062 & 1.054 & 13 & 84 & 0.43\\\n&W & 1.793 & 0.721 & 69.7 & 0.726 & 0.631 & 19 & 34 & 0.44\\\n1328$+$307 &K & 5.438 & 3.117 & 83.2 & 0.819 & 0.401 & 24 & 17 & 0.63\\\n&Q & 2.682 & 1.494 & 86.0 & 0.067 & 0.061 & 7 & 9 & 0.67\\\n&W & 1.473 & 0.705 & $-$70.7 & 0.084 & 0.081 & 6 & 14 & 0.47\\\n&D & 0.966 & 0.507 & $-$60.5 & 0.189 & 0.190 & 14 & 13 & 0.45\\\n1343$+$451 &K & 5.258 & 3.243 & 86.2 & 0.820 & 0.819 & 8 & 100 & 0.68\\\n&Q & 2.626 & 1.559 & 89.7 & 0.585 & 0.551 & 12 & 46 & 0.57\\\n&W & 1.313 & 0.766 & $-$83.6 & 0.333 & 0.262 & 21 & 12 & 0.48\\\n&D & 0.853 & 0.544 & $-$76.3 & 0.274 & 0.267 & 16 & 17 & 0.60\\\n1611$+$343 &K & 6.967 & 3.088 & 66.1 & 4.018 & 3.331 & 19 & 172 & 0.67\\\n&Q & 3.524 & 1.486 & 67.0 & 2.244 & 2.106 & 34 & 61 & 0.63\\\n&W & 1.792 & 0.727 & 68.2 & 1.315 & 1.191 & 38 & 32 & 0.55\\\n&D & 1.684 & 0.515 & 65.6 & 0.309 & 0.324 & 70 & 5 & 0.47\\\n1633$+$382 &K & 6.263 & 3.389 & 65.5 & 5.233 & 5.170 & 34 & 151 & 0.70\\\n&Q & 3.303 & 1.644 & 63.6 & 5.500 & 5.502 & 61 & 91 & 0.72\\\n&W & 1.705 & 0.818 & 62.5 & 4.837 & 4.476 & 35 & 127 & 0.62\\\n&D & 1.023 & 0.538 & 73.8 & 3.056 & 3.002 & 54 & 55 & 0.62\\\n1641$+$399 &K & 5.053 & 3.521 & $-$81.7 & 4.866 & 4.200 & 40 & 104 & 0.63\\\n&Q & 2.524 & 1.697 & $-$85.5 & 3.695 & 3.231 & 31 & 106 & 0.62\\\n&W & 1.251 & 0.832 & $-$81.2 & 2.390 & 1.875 & 22 & 85 & 0.66\\\n&D & 0.974 & 0.568 & 80.3 & 1.257 & 1.253 & 44 & 29 & 0.59\\\n1749$+$096 &K & 5.135 & 3.567 & $-$83.9 & 2.933 & 2.829 & 12 & 230 & 0.62\\\n&Q & 2.621 & 1.717 & $-$86.6 & 2.560 & 2.390 & 13 & 181 & 0.67\\\n&W & 1.350 & 0.821 & $-$80.5 & 1.891 & 1.502 & 26 & 58 & 0.77\\\n&D & 0.885 & 0.568 & $-$78.0 & 1.174 & 1.124 & 41 & 28 & 0.65\\\n1921$-$293 &K & 6.856 & 5.243 & $-$22.3 & 7.553 & 7.452 & 77 & 97 & 0.57\\\n&Q & 3.466 & 2.604 & $-$17.4 & 5.092 & 4.822 & 27 & 178 & 0.62\\\n&W & 1.841 & 1.252 & $-$18.8 & 3.012 & 2.246 & 87 & 26 & 0.61\\\n&D & 1.320 & 0.798 & $-$23.4 & 1.549 & 1.542 & 81 & 19 & 0.49\\\n2200$+$420 &K & 5.575 & 3.196 & 87.6 & 5.239 & 4.573 & 20 & 223 & 0.70\\\n&Q & 2.799 & 1.588 & 81.0 & 4.674 & 4.271 & 28 & 152 & 0.64\\\n&W & 1.423 & 0.776 & 77.9 & 3.458 & 3.497 & 94 & 37 & 0.70\\\n&D & 0.900 & 0.546 & $-$84.4 & 2.253 & 2.190 & 101 & 22 & 0.61\\\n2223$-$052 &K & 5.495 & 3.886 & 78.0 & 2.312 & 2.242 & 10 & 222 & 0.56\\\n&Q & 2.827 & 1.878 & 81.0 & 1.452 & 1.361 & 6 & 213 & 0.56\\\n&W & 1.446 & 0.921 & 82.0 & 0.629 & 0.604 & 16 & 39 & 0.65\\\n&D & 0.909 & 0.650 & $-$70.3 & 0.267 & 0.253 & 22 & 11 & 0.52\\\n2230$+$114 &K & 5.268 & 3.409 & $-$88.0 & 2.313 & 2.088 & 10 & 208 & 0.59\\\n&Q & 2.689 & 1.642 & 87.6 & 2.138 & 2.023 & 15 & 138 & 0.70\\\n&W & 1.354 & 0.792 & 82.1 & 1.506 & 1.519 & 30 & 51 & 0.61\\\n&D & 0.876 & 0.564 & $-$72.3 & 1.568 & 1.089 & 18 & 59 & 0.59\\\n2251$+$158 &K & 5.205 & 3.419 & $-$81.5 & 7.036 & 6.044 & 25 & 239 & 0.54\\\n&Q & 2.722 & 1.582 & $-$84.1 & 9.040 & 8.790 & 42 & 209 & 0.61\\\n&W & 1.348 & 0.781 & $-$86.3 & 8.404 & 8.067 & 64 & 126 & 0.75\\\n&D & 0.901 & 0.553 & $-$82.8 & 6.520 & 5.975 & 67 & 89 & 0.62\\\n\n[lccccrrrr]{} 0234+285 & K & C & 2.951$\\pm$0.111 & 2.816$\\pm$0.077 & 0.876$\\pm$0.024 & ... & ... & 1.394$\\pm$ 0.076\\\n& & J2 & 0.084$\\pm$0.018 & 0.085$\\pm$0.013 & $<$[*0.602*]{} & 3.741$\\pm$0.046 & 1.4$\\pm$0.7 & $>$[*0.084*]{}\\\n& Q & C & 2.290$\\pm$0.322 & 2.050$\\pm$0.215 & 0.629$\\pm$0.066 & ... & ... & 2.098$\\pm$ 0.440\\\n& & J1 & 0.111$\\pm$0.095 & 0.123$\\pm$0.070 & $<$[*1.171*]{} & 1.820$\\pm$0.334 & -26.1$\\pm$10.4 & $>$[*0.029*]{}\\\n& W & C & 1.522$\\pm$0.125 & 1.218$\\pm$0.078 & 0.468$\\pm$0.030 & ... & ... & 2.519$\\pm$ 0.323\\\n& D & C & 0.839$\\pm$0.060 & 0.785$\\pm$0.041 & 0.183$\\pm$0.010 & ... & ... & 9.080$\\pm$ 0.949\\\n0235+164 & K & C & 0.884$\\pm$0.027 & 0.857$\\pm$0.019 & 0.744$\\pm$0.016 & ... & ... & 0.509$\\pm$ 0.022\\\n& Q & C & 0.846$\\pm$0.028 & 0.756$\\pm$0.018 & 0.698$\\pm$0.017 & ... & ... & 0.553$\\pm$ 0.027\\\n& W & C & 0.496$\\pm$0.069 & 0.420$\\pm$0.045 & 0.408$\\pm$0.043 & ... & ... & 0.950$\\pm$ 0.202\\\n& D & C & 0.314$\\pm$0.149 & 0.275$\\pm$0.098 & 0.361$\\pm$0.128 & ... & ... & 0.768$\\pm$ 0.551\\\n0316+413 & K & C & 28.231$\\pm$1.670 & 22.837$\\pm$1.050 & 1.770$\\pm$0.081 & ... & ... & 1.507$\\pm$ 0.139\\\n& & J1 & 1.481$\\pm$0.175 & 1.435$\\pm$0.122 & 0.713$\\pm$0.061 & 2.991$\\pm$0.030 & 1.7$\\pm$0.6 & 0.487$\\pm$ 0.083\\\n& & J2 & 0.408$\\pm$0.300 & 0.458$\\pm$0.224 & $<$[*2.004*]{} & 6.403$\\pm$0.490 & -129.2$\\pm$4.4 & $>$[*0.017*]{}\\\n& Q & C & 7.317$\\pm$1.670 & 5.894$\\pm$1.047 & 0.855$\\pm$0.152 & ... & ... & 1.673$\\pm$ 0.596\\\n& & J3 & 11.060$\\pm$2.242 & 11.175$\\pm$1.593 & $<$[*0.281*]{} & 1.985$\\pm$0.020 & -178.9$\\pm$0.6 & $>$[*23.345*]{}\\\n& W & C & 6.029$\\pm$1.303 & 4.497$\\pm$0.779 & 0.517$\\pm$0.090 & ... & ... & 3.771$\\pm$ 1.308\\\n& & J3 & 8.149$\\pm$1.490 & 3.340$\\pm$0.565 & 0.928$\\pm$0.157 & 2.413$\\pm$0.079 & 179.1$\\pm$1.9 & 1.582$\\pm$ 0.535\\\n& D & C & 3.795$\\pm$0.329 & 3.246$\\pm$0.214 & 0.276$\\pm$0.018 & ... & ... & 8.329$\\pm$ 1.097\\\n& & J3 & 2.977$\\pm$0.313 & 1.830$\\pm$0.164 & 0.487$\\pm$0.044 & 2.444$\\pm$0.022 & 177.3$\\pm$0.5 & 2.099$\\pm$ 0.376\\\n& & J4 & 0.469$\\pm$0.186 & 0.338$\\pm$0.109 & 0.441$\\pm$0.142 & 1.559$\\pm$0.071 & 177.9$\\pm$2.6 & 0.403$\\pm$ 0.260\\\n& & J5 & 0.689$\\pm$0.374 & 0.288$\\pm$0.144 & 0.700$\\pm$0.351 & 0.812$\\pm$0.175 & 150.6$\\pm$12.2 & 0.235$\\pm$ 0.236\\\n0415+379 & K & C & 3.934$\\pm$0.344 & 3.940$\\pm$0.243 & $<$[*0.255*]{} & ... & ... & $>$[*10.466*]{}\\\n& & J1 & 0.237$\\pm$0.119 & 0.250$\\pm$0.086 & $<$[*1.460*]{} & 6.446$\\pm$0.252 & 64.5$\\pm$2.2 & $>$[*0.019*]{}\\\n& Q & C & 3.696$\\pm$0.394 & 3.708$\\pm$0.279 & $<$[*0.156*]{} & ... & ... & $>$[*26.125*]{}\\\n& W & C & 3.894$\\pm$0.090 & 3.712$\\pm$0.062 & 0.219$\\pm$0.004 & ... & ... & 13.994$\\pm$ 0.471\\\n& D & C & 2.749$\\pm$0.047 & 2.688$\\pm$0.033 & 0.102$\\pm$0.001 & ... & ... & 45.541$\\pm$ 1.124\\\n0420-014 & K & C & 5.113$\\pm$0.064 & 5.058$\\pm$0.045 & 0.463$\\pm$0.004 & ... & ... & 7.508$\\pm$ 0.134\\\n& Q & C & 4.046$\\pm$0.132 & 3.777$\\pm$0.090 & 0.574$\\pm$0.014 & ... & ... & 3.866$\\pm$ 0.184\\\n& W & C & 2.402$\\pm$0.711 & 2.453$\\pm$0.508 & $<$[*0.227*]{} & ... & ... & $>$[*14.685*]{}\\\n& D & C & 1.643$\\pm$0.164 & 1.616$\\pm$0.115 & 0.110$\\pm$0.008 & ... & ... & 42.745$\\pm$ 6.083\\\n0528+134 & K & C & 1.147$\\pm$0.083 & 1.149$\\pm$0.059 & $<$[*0.203*]{} & ... & ... & $>$[*14.053*]{}\\\n& & J1 & 0.179$\\pm$0.096 & 0.066$\\pm$0.033 & 4.406$\\pm$2.224 & 4.543$\\pm$1.112 & 37.6$\\pm$13.8 & 0.005$\\pm$ 0.005\\\n& Q & C & 0.935$\\pm$0.045 & 0.878$\\pm$0.031 & 0.520$\\pm$0.018 & ... & ... & 1.744$\\pm$ 0.122\\\n& W & C & 0.614$\\pm$0.054 & 0.519$\\pm$0.035 & 0.420$\\pm$0.028 & ... & ... & 1.756$\\pm$ 0.238\\\n& D & C & 0.333$\\pm$0.069 & 0.336$\\pm$0.049 & $<$[*0.097*]{} & ... & ... & $>$[*17.823*]{}\\\n0716+714 & K & C & 2.490$\\pm$0.465 & 2.511$\\pm$0.330 & $<$[*0.616*]{} & ... & ... & $>$[*1.213*]{}\\\n& Q & C & 2.733$\\pm$0.047 & 2.654$\\pm$0.033 & 0.427$\\pm$0.005 & ... & ... & 2.775$\\pm$ 0.069\\\n& W & C & 2.061$\\pm$0.041 & 2.045$\\pm$0.029 & 0.109$\\pm$0.002 & ... & ... & 32.119$\\pm$ 0.902\\\n& D & C & 1.436$\\pm$0.034 & 1.425$\\pm$0.024 & 0.073$\\pm$0.001 & ... & ... & 49.894$\\pm$ 1.679\\\n0727-115 & K & C & 3.848$\\pm$0.126 & 3.724$\\pm$0.088 & 0.866$\\pm$0.020 & ... & ... & 2.184$\\pm$ 0.103\\\n& & J1 & 0.101$\\pm$0.048 & 0.108$\\pm$0.035 & $<$[*1.587*]{} & 3.822$\\pm$0.258 & -82.9$\\pm$3.9 & $>$[*0.017*]{}\\\n& Q & C & 2.367$\\pm$0.044 & 2.292$\\pm$0.031 & 0.428$\\pm$0.006 & ... & ... & 5.500$\\pm$ 0.148\\\n& W & C & 1.146$\\pm$0.198 & 1.155$\\pm$0.141 & $<$[*0.143*]{} & ... & ... & $>$[*23.705*]{}\\\n& D & C & 0.786$\\pm$0.025 & 0.766$\\pm$0.018 & 0.129$\\pm$0.003 & ... & ... & 20.106$\\pm$ 0.931\\\n0735+178 & K & C & 1.000$\\pm$0.090 & 1.002$\\pm$0.063 & $<$[*0.274*]{} & ... & ... & $>$[*3.167*]{}\\\n& & J1 & 0.104$\\pm$0.033 & 0.052$\\pm$0.015 & 3.588$\\pm$1.005 & 4.290$\\pm$0.502 & 71.7$\\pm$6.7 & 0.002$\\pm$ 0.001\\\n& Q & C & 0.908$\\pm$0.045 & 0.819$\\pm$0.030 & 0.659$\\pm$0.024 & ... & ... & 0.498$\\pm$ 0.037\\\n& W & C & 0.738$\\pm$0.079 & 0.551$\\pm$0.047 & 0.550$\\pm$0.047 & ... & ... & 0.581$\\pm$ 0.099\\\n& D & C & 0.426$\\pm$0.031 & 0.380$\\pm$0.021 & 0.229$\\pm$0.012 & ... & ... & 1.935$\\pm$ 0.211\\\n& & J1 & 0.068$\\pm$0.017 & 0.068$\\pm$0.012 & $<$[*0.118*]{} & 0.645$\\pm$0.010 & 29.7$\\pm$0.9 & $>$[*1.169*]{}\\\n0827+243 & K & C & 0.905$\\pm$0.027 & 0.868$\\pm$0.019 & 0.912$\\pm$0.020 & ... & ... & 0.347$\\pm$ 0.015\\\n& Q & C & 0.667$\\pm$0.039 & 0.592$\\pm$0.026 & 0.727$\\pm$0.032 & ... & ... & 0.403$\\pm$ 0.035\\\n& W & C & 0.324$\\pm$0.028 & 0.267$\\pm$0.018 & 0.467$\\pm$0.032 & ... & ... & 0.474$\\pm$ 0.064\\\n& D & C & 0.287$\\pm$0.015 & 0.275$\\pm$0.011 & 0.158$\\pm$0.006 & ... & ... & 3.668$\\pm$ 0.286\\\n0836+710 & K & C & 1.994$\\pm$0.141 & 1.633$\\pm$0.089 & 2.265$\\pm$0.124 & ... & ... & 0.205$\\pm$ 0.023\\\n& & J1 & 0.061$\\pm$0.027 & 0.065$\\pm$0.020 & $<$[*1.470*]{} & 4.698$\\pm$0.227 & -136.9$\\pm$2.8 & $>$[*0.015*]{}\\\n& Q & C & 1.065$\\pm$0.029 & 1.048$\\pm$0.021 & 0.317$\\pm$0.006 & ... & ... & 5.603$\\pm$ 0.221\\\n& & J2 & 0.137$\\pm$0.017 & 0.137$\\pm$0.012 & 0.213$\\pm$0.018 & 2.458$\\pm$0.009 & -140.1$\\pm$0.2 & 1.596$\\pm$ 0.274\\\n& W & C & 0.656$\\pm$0.160 & 0.590$\\pm$0.107 & 0.460$\\pm$0.083 & ... & ... & 1.639$\\pm$ 0.596\\\n& D & C & 0.519$\\pm$0.060 & 0.335$\\pm$0.032 & 0.566$\\pm$0.055 & ... & ... & 0.857$\\pm$ 0.165\\\n& & J3 & 0.053$\\pm$0.007 & 0.044$\\pm$0.005 & 0.359$\\pm$0.038 & 0.954$\\pm$0.019 & -153.8$\\pm$1.1 & 0.217$\\pm$ 0.046\\\n0851+202 & K & C & 4.707$\\pm$0.435 & 4.714$\\pm$0.307 & $<$[*0.266*]{} & ... & ... & $>$[*14.244*]{}\\\n& & J1 & 0.252$\\pm$0.134 & 0.123$\\pm$0.059 & 3.476$\\pm$1.659 & 4.026$\\pm$0.829 & -107.2$\\pm$11.6 & 0.004$\\pm$ 0.004\\\n& Q & C & 3.838$\\pm$0.089 & 3.683$\\pm$0.062 & 0.414$\\pm$0.007 & ... & ... & 4.805$\\pm$ 0.162\\\n& W & C & 2.755$\\pm$0.112 & 2.453$\\pm$0.074 & 0.345$\\pm$0.010 & ... & ... & 4.966$\\pm$ 0.301\\\n& D & C & 1.764$\\pm$0.106 & 1.653$\\pm$0.073 & 0.179$\\pm$0.008 & ... & ... & 11.813$\\pm$ 1.041\\\n0923+392 & K & C & 0.552$\\pm$0.123 & 6.518$\\pm$0.123 & 3.812$\\pm$0.072 & ... & ... & 0.011$\\pm$ 0.001\\\n& & J1 & 7.994$\\pm$18.767 & 0.262$\\pm$0.615 & $<$[*0.326*]{} & 5.683$\\pm$0.383 & 100.3$\\pm$3.9 & $>$[*20.917*]{}\\\n& Q & C & 0.743$\\pm$0.127 & 0.237$\\pm$0.039 & 1.147$\\pm$0.187 & ... & ... & 0.157$\\pm$ 0.051\\\n& & J1 & 5.222$\\pm$2.652 & 0.555$\\pm$0.280 & 0.607$\\pm$0.307 & 3.174$\\pm$0.153 & 100.6$\\pm$2.8 & 3.947$\\pm$ 3.986\\\n& W & C & 0.509$\\pm$0.056 & 0.501$\\pm$0.039 & 0.755$\\pm$0.059 & ... & ... & 0.249$\\pm$ 0.039\\\n& & J1 & 3.309$\\pm$2.701 & 0.301$\\pm$0.245 & 0.629$\\pm$0.511 & 2.779$\\pm$0.256 & 98.3$\\pm$5.3 & 2.329$\\pm$ 3.787\\\n& D & C & 1.899$\\pm$0.306 & 1.141$\\pm$0.158 & 0.555$\\pm$0.077 & ... & ... & 1.717$\\pm$ 0.475\\\n1055+018 & K & C & 2.849$\\pm$0.262 & 2.856$\\pm$0.185 & $<$[*0.269*]{} & ... & ... & $>$[*12.239*]{}\\\n& Q & C & 2.438$\\pm$0.071 & 2.348$\\pm$0.049 & 0.438$\\pm$0.009 & ... & ... & 3.942$\\pm$ 0.166\\\n& W & C & 1.717$\\pm$0.064 & 1.475$\\pm$0.041 & 0.426$\\pm$0.012 & ... & ... & 2.935$\\pm$ 0.165\\\n& D & C & 1.068$\\pm$0.030 & 1.047$\\pm$0.021 & 0.103$\\pm$0.002 & ... & ... & 31.226$\\pm$ 1.233\\\n1101+384 & K & C & 0.442$\\pm$0.019 & 0.435$\\pm$0.013 & 0.530$\\pm$0.016 & ... & ... & 0.266$\\pm$ 0.016\\\n& Q & C & 0.347$\\pm$0.018 & 0.311$\\pm$0.012 & 0.661$\\pm$0.025 & ... & ... & 0.134$\\pm$ 0.010\\\n& W & C & 0.222$\\pm$0.052 & 0.187$\\pm$0.034 & 0.438$\\pm$0.079 & ... & ... & 0.196$\\pm$ 0.071\\\n& D & C & 0.365$\\pm$0.018 & 0.348$\\pm$0.012 & 0.151$\\pm$0.005 & ... & ... & 2.711$\\pm$ 0.188\\\n1127-145 & K & C & 2.074$\\pm$0.144 & 2.068$\\pm$0.102 & $<$[*0.273*]{} & ... & ... & $>$[*10.012*]{}\\\n& Q & C & 1.837$\\pm$0.213 & 1.794$\\pm$0.149 & 0.464$\\pm$0.039 & ... & ... & 3.062$\\pm$ 0.509\\\n& W & C & 1.391$\\pm$0.285 & 1.406$\\pm$0.203 & $<$[*0.197*]{} & ... & ... & $>$[*12.913*]{}\\\n& D & C & 0.747$\\pm$0.087 & 0.749$\\pm$0.061 & $<$[*0.074*]{} & ... & ... & $>$[*48.720*]{}\\\n1156+295 & K & C & 0.866$\\pm$0.027 & 0.853$\\pm$0.019 & 0.496$\\pm$0.011 & ... & ... & 0.998$\\pm$ 0.044\\\n& Q & C & 0.892$\\pm$0.044 & 0.809$\\pm$0.030 & 0.624$\\pm$0.023 & ... & ... & 0.649$\\pm$ 0.048\\\n& W & C & 0.790$\\pm$0.064 & 0.635$\\pm$0.040 & 0.462$\\pm$0.029 & ... & ... & 1.049$\\pm$ 0.132\\\n& D & C & 0.490$\\pm$0.032 & 0.481$\\pm$0.022 & 0.095$\\pm$0.004 & ... & ... & 15.387$\\pm$ 1.418\\\n1222+216 & K & C & 2.351$\\pm$0.044 & 2.287$\\pm$0.031 & 0.713$\\pm$0.010 & ... & ... & 1.090$\\pm$ 0.029\\\n& Q & C & 1.734$\\pm$0.090 & 1.495$\\pm$0.059 & 0.792$\\pm$0.031 & ... & ... & 0.651$\\pm$ 0.051\\\n& & J1 & 0.175$\\pm$0.019 & 0.171$\\pm$0.013 & 0.356$\\pm$0.028 & 1.603$\\pm$0.014 & 13.6$\\pm$0.5 & 0.325$\\pm$ 0.051\\\n& W & C & 0.872$\\pm$0.109 & 0.776$\\pm$0.073 & 0.336$\\pm$0.031 & ... & ... & 1.820$\\pm$ 0.341\\\n& & J1 & 0.253$\\pm$0.072 & 0.258$\\pm$0.051 & $<$[*0.195*]{} & 0.981$\\pm$0.019 & 4.2$\\pm$1.1 & $>$[*1.575*]{}\\\n& D & C & 0.403$\\pm$0.136 & 0.426$\\pm$0.099 & $<$[*0.187*]{} & ... & ... & $>$[*2.708*]{}\\\n& & J1 & 0.123$\\pm$0.057 & 0.123$\\pm$0.040 & $<$[*0.247*]{} & 0.925$\\pm$0.040 & -14.1$\\pm$2.5 & $>$[*0.473*]{}\\\n1226+023 & K & C & 6.945$\\pm$0.810 & 6.391$\\pm$0.548 & 1.307$\\pm$0.112 & ... & ... & 0.774$\\pm$ 0.133\\\n& & J3 & 1.511$\\pm$0.375 & 1.538$\\pm$0.268 & $<$[*0.745*]{} & 4.120$\\pm$0.065 & -136.2$\\pm$0.9 & $>$[*0.519*]{}\\\n& Q & C & 4.749$\\pm$0.062 & 4.688$\\pm$0.044 & 0.259$\\pm$0.002 & ... & ... & 13.472$\\pm$ 0.251\\\n& & J2 & 0.823$\\pm$0.041 & 0.800$\\pm$0.029 & 0.377$\\pm$0.014 & 1.962$\\pm$0.007 & -140.2$\\pm$0.2 & 1.102$\\pm$ 0.079\\\n& & J3 & 0.958$\\pm$0.054 & 0.675$\\pm$0.031 & 1.386$\\pm$0.064 & 4.344$\\pm$0.032 & -143.5$\\pm$0.4 & 0.095$\\pm$ 0.009\\\n& & J4 & 1.373$\\pm$0.212 & 0.350$\\pm$0.052 & 3.064$\\pm$0.459 & 7.402$\\pm$0.230 & -141.9$\\pm$1.8 & 0.028$\\pm$ 0.008\\\n& & J5 & 0.720$\\pm$0.161 & 0.291$\\pm$0.060 & 2.353$\\pm$0.487 & 10.642$\\pm$0.243 & -141.6$\\pm$1.3 & 0.025$\\pm$ 0.010\\\n& W & C & 2.987$\\pm$0.248 & 2.144$\\pm$0.145 & 0.641$\\pm$0.043 & ... & ... & 1.383$\\pm$ 0.187\\\n& & J1 & 1.293$\\pm$0.246 & 0.852$\\pm$0.135 & 0.709$\\pm$0.113 & 1.043$\\pm$0.056 & -138.2$\\pm$3.1 & 0.489$\\pm$ 0.156\\\n& & J2 & 0.184$\\pm$0.096 & 0.198$\\pm$0.071 & $<$[*0.398*]{} & 1.931$\\pm$0.071 & -143.1$\\pm$2.1 & $>$[*0.221*]{}\\\n& D & C & 1.829$\\pm$0.225 & 1.605$\\pm$0.149 & 0.279$\\pm$0.026 & ... & ... & 4.471$\\pm$ 0.829\\\n& & J1 & 0.936$\\pm$0.403 & 0.427$\\pm$0.167 & 0.704$\\pm$0.276 & 0.903$\\pm$0.138 & -143.1$\\pm$8.7 & 0.359$\\pm$ 0.282\\\n1228+126 & K & C & 1.837$\\pm$0.210 & 1.844$\\pm$0.149 & $<$[*0.321*]{} & ... & ... & $>$[*2.933*]{}\\\n& & J1 & 0.199$\\pm$0.013 & 0.198$\\pm$0.009 & 0.408$\\pm$0.018 & 5.115$\\pm$0.009 & -69.7$\\pm$0.1 & 0.197$\\pm$ 0.018\\\n& Q & C & 1.286$\\pm$0.197 & 1.295$\\pm$0.140 & $<$[*0.213*]{} & ... & ... & $>$[*4.690*]{}\\\n& & J1 & 0.098$\\pm$0.034 & 0.090$\\pm$0.023 & $<$[*0.449*]{} & 3.023$\\pm$0.057 & -70.0$\\pm$1.1 & $>$[*0.080*]{}\\\n& W & C & 1.068$\\pm$0.049 & 0.947$\\pm$0.033 & 0.362$\\pm$0.012 & ... & ... & 1.345$\\pm$ 0.093\\\n& D & C & 0.657$\\pm$0.073 & 0.659$\\pm$0.051 & $<$[*0.054*]{} & ... & ... & $>$[*37.271*]{}\\\n1253-055 & K & C & 30.173$\\pm$1.175 & 26.605$\\pm$0.777 & 1.882$\\pm$0.055 & ... & ... & 2.150$\\pm$ 0.126\\\n& Q & C & 20.803$\\pm$0.811 & 18.545$\\pm$0.540 & 0.857$\\pm$0.025 & ... & ... & 7.148$\\pm$ 0.416\\\n& & J1 & 1.888$\\pm$0.356 & 1.720$\\pm$0.240 & 0.843$\\pm$0.118 & 2.106$\\pm$0.059 & -137.2$\\pm$1.6 & 0.670$\\pm$ 0.187\\\n& W & C & 7.396$\\pm$1.100 & 6.780$\\pm$0.743 & 0.300$\\pm$0.033 & 0.287$\\pm$0.016 & 28.3$\\pm$3.3 & 20.738$\\pm$ 4.553\\\n& & J1 & 5.256$\\pm$1.195 & 5.320$\\pm$0.850 & $<$[*0.183*]{} & 0.454$\\pm$0.015 & -152.8$\\pm$1.8 & $>$[*39.733*]{}\\\n& D & C & 7.699$\\pm$1.481 & 4.123$\\pm$0.699 & 0.591$\\pm$0.100 & ... & ... & 5.562$\\pm$ 1.887\\\n& & J1 & 2.372$\\pm$0.688 & 2.426$\\pm$0.492 & $<$[*0.153*]{} & 0.726$\\pm$0.016 & -153.7$\\pm$1.2 & $>$[*25.569*]{}\\\n1308+326 & K & C & 1.436$\\pm$0.405 & 1.464$\\pm$0.289 & $<$[*0.851*]{} & ... & ... & $>$[*0.650*]{}\\\n& Q & C & 1.105$\\pm$0.030 & 1.055$\\pm$0.021 & 0.434$\\pm$0.009 & ... & ... & 1.925$\\pm$ 0.077\\\n& W & C & 0.740$\\pm$0.113 & 0.615$\\pm$0.072 & 0.442$\\pm$0.052 & ... & ... & 1.243$\\pm$ 0.292\\\n1328+307 & K & C & 0.602$\\pm$0.194 & 0.375$\\pm$0.103 & 2.917$\\pm$0.798 & ... & ... & 0.021$\\pm$ 0.012\\\n& & J1 & 0.453$\\pm$0.070 & 0.283$\\pm$0.037 & 2.875$\\pm$0.376 & 5.248$\\pm$0.188 & 43.2$\\pm$2.1 & 0.017$\\pm$ 0.004\\\n& Q & C & 0.083$\\pm$0.015 & 0.061$\\pm$0.009 & 1.106$\\pm$0.166 & ... & ... & 0.021$\\pm$ 0.006\\\n& W & C & 0.102$\\pm$0.010 & 0.081$\\pm$0.006 & 0.472$\\pm$0.037 & ... & ... & 0.139$\\pm$ 0.022\\\n& D & C & 0.195$\\pm$0.020 & 0.190$\\pm$0.014 & 0.122$\\pm$0.009 & ... & ... & 3.973$\\pm$ 0.586\\\n1343+451 & K & C & 0.826$\\pm$0.026 & 0.819$\\pm$0.018 & 0.382$\\pm$0.008 & ... & ... & 3.287$\\pm$ 0.146\\\n& Q & C & 0.607$\\pm$0.037 & 0.549$\\pm$0.025 & 0.649$\\pm$0.029 & ... & ... & 0.837$\\pm$ 0.075\\\n& W & C & 0.326$\\pm$0.060 & 0.250$\\pm$0.036 & 0.499$\\pm$0.073 & ... & ... & 0.760$\\pm$ 0.221\\\n& D & C & 0.279$\\pm$0.024 & 0.267$\\pm$0.017 & 0.148$\\pm$0.009 & ... & ... & 7.395$\\pm$ 0.927\\\n1611+343 & K & C & 3.229$\\pm$0.386 & 3.242$\\pm$0.273 & $<$[*0.368*]{} & ... & ... & $>$[*9.380*]{}\\\n& & J1 & 0.723$\\pm$0.129 & 0.582$\\pm$0.081 & 1.940$\\pm$0.271 & 4.360$\\pm$0.135 & 163.9$\\pm$1.8 & 0.076$\\pm$ 0.021\\\n& & J2 & 0.258$\\pm$0.102 & 0.173$\\pm$0.057 & 3.041$\\pm$1.001 & 3.443$\\pm$0.500 & -132.2$\\pm$8.3 & 0.011$\\pm$ 0.007\\\n& Q & C & 2.317$\\pm$0.144 & 2.085$\\pm$0.096 & 0.678$\\pm$0.031 & ... & ... & 1.987$\\pm$ 0.184\\\n& W & C & 1.508$\\pm$0.126 & 1.186$\\pm$0.078 & 0.509$\\pm$0.033 & ... & ... & 2.295$\\pm$ 0.301\\\n& D & C & 0.327$\\pm$0.036 & 0.324$\\pm$0.026 & 0.097$\\pm$0.008 & ... & ... & 13.703$\\pm$ 2.171\\\n1633+382 & K & C & 5.266$\\pm$0.104 & 5.172$\\pm$0.073 & 0.608$\\pm$0.009 & ... & ... & 6.584$\\pm$ 0.185\\\n& Q & C & 5.856$\\pm$0.112 & 5.503$\\pm$0.077 & 0.559$\\pm$0.008 & ... & ... & 8.661$\\pm$ 0.241\\\n& W & C & 5.104$\\pm$0.188 & 4.457$\\pm$0.124 & 0.416$\\pm$0.012 & ... & ... & 13.630$\\pm$ 0.757\\\n& D & C & 3.247$\\pm$0.145 & 3.004$\\pm$0.099 & 0.202$\\pm$0.007 & ... & ... & 36.776$\\pm$ 2.418\\\n1641+399 & K & C & 4.406$\\pm$0.236 & 4.184$\\pm$0.163 & 0.998$\\pm$0.039 & ... & ... & 1.158$\\pm$ 0.090\\\n& & J4 & 0.960$\\pm$0.333 & 0.526$\\pm$0.160 & 3.537$\\pm$1.077 & 5.955$\\pm$0.538 & -84.5$\\pm$5.2 & 0.020$\\pm$ 0.012\\\n& Q & C & 3.432$\\pm$0.210 & 3.225$\\pm$0.144 & 0.534$\\pm$0.024 & ... & ... & 3.150$\\pm$ 0.281\\\n& & J3 & 0.372$\\pm$0.102 & 0.308$\\pm$0.065 & 0.940$\\pm$0.198 & 2.667$\\pm$0.099 & -90.7$\\pm$2.1 & 0.110$\\pm$ 0.047\\\n& W & C & 1.930$\\pm$0.141 & 1.879$\\pm$0.098 & 0.162$\\pm$0.008 & ... & ... & 19.247$\\pm$ 2.016\\\n& & J1 & 0.118$\\pm$0.038 & 0.123$\\pm$0.027 & $<$[*0.219*]{} & 0.787$\\pm$0.024 & -128.9$\\pm$1.8 & $>$[*0.644*]{}\\\n& & J2 & 0.363$\\pm$0.102 & 0.370$\\pm$0.073 & $<$[*0.190*]{} & 1.340$\\pm$0.019 & -92.2$\\pm$0.8 & $>$[*2.630*]{}\\\n& & J3 & 0.159$\\pm$0.032 & 0.148$\\pm$0.022 & 0.316$\\pm$0.047 & 2.169$\\pm$0.024 & -76.7$\\pm$0.6 & 0.417$\\pm$ 0.124\\\n& D & C & 1.215$\\pm$0.392 & 1.254$\\pm$0.281 & $<$[*0.160*]{} & ... & ... & $>$[*12.434*]{}\\\n1749+096 & K & C & 2.799$\\pm$0.352 & 2.808$\\pm$0.249 & $<$[*0.357*]{} & ... & ... & $>$[*4.766*]{}\\\n& & J1 & 0.145$\\pm$0.082 & 0.091$\\pm$0.043 & 3.503$\\pm$1.671 & 3.845$\\pm$0.835 & 48.9$\\pm$12.3 & 0.003$\\pm$ 0.002\\\n& Q & C & 2.718$\\pm$0.158 & 2.382$\\pm$0.104 & 0.795$\\pm$0.035 & ... & ... & 0.934$\\pm$ 0.082\\\n& W & C & 1.700$\\pm$0.523 & 1.465$\\pm$0.341 & 0.470$\\pm$0.110 & ... & ... & 1.671$\\pm$ 0.782\\\n& D & C & 1.273$\\pm$0.318 & 1.125$\\pm$0.211 & 0.284$\\pm$0.053 & ... & ... & 3.428$\\pm$ 1.288\\\n1921-293 & K & C & 8.091$\\pm$0.297 & 7.456$\\pm$0.201 & 1.808$\\pm$0.049 & ... & ... & 0.550$\\pm$ 0.030\\\n& Q & C & 5.223$\\pm$0.354 & 4.816$\\pm$0.240 & 0.888$\\pm$0.044 & ... & ... & 1.472$\\pm$ 0.147\\\n& & J2 & 0.271$\\pm$0.103 & 0.281$\\pm$0.074 & $<$[*0.761*]{} & 3.089$\\pm$0.101 & 24.2$\\pm$1.9 & $>$[*0.104*]{}\\\n& W & C & 2.004$\\pm$0.553 & 2.043$\\pm$0.395 & $<$[*0.279*]{} & ... & ... & $>$[*5.739*]{}\\\n& & J1 & 1.170$\\pm$0.351 & 0.609$\\pm$0.162 & 1.280$\\pm$0.340 & 1.428$\\pm$0.170 & 4.2$\\pm$6.8 & 0.159$\\pm$ 0.084\\\n& D & C & 1.697$\\pm$0.087 & 1.543$\\pm$0.058 & 0.320$\\pm$0.012 & ... & ... & 3.683$\\pm$ 0.278\\\n2200+420 & K & C & 4.838$\\pm$0.322 & 4.544$\\pm$0.220 & 1.055$\\pm$0.051 & ... & ... & 0.763$\\pm$ 0.074\\\n& & J2 & 0.605$\\pm$0.087 & 0.499$\\pm$0.055 & 1.859$\\pm$0.206 & 4.017$\\pm$0.103 & -163.8$\\pm$1.5 & 0.031$\\pm$ 0.007\\\n& Q & C & 4.351$\\pm$0.164 & 4.231$\\pm$0.114 & 0.350$\\pm$0.009 & ... & ... & 6.236$\\pm$ 0.337\\\n& & J1 & 0.499$\\pm$0.112 & 0.283$\\pm$0.055 & 1.623$\\pm$0.316 & 2.038$\\pm$0.158 & -161.0$\\pm$4.4 & 0.033$\\pm$ 0.013\\\n& W & C & 3.925$\\pm$0.094 & 3.498$\\pm$0.063 & 0.352$\\pm$0.006 & ... & ... & 5.561$\\pm$ 0.199\\\n& D & C & 2.326$\\pm$0.122 & 2.191$\\pm$0.084 & 0.174$\\pm$0.007 & ... & ... & 13.488$\\pm$ 1.029\\\n2223-052 & K & C & 2.240$\\pm$0.164 & 2.244$\\pm$0.116 & $<$[*0.225*]{} & ... & ... & $>$[*17.503*]{}\\\n& & J2 & 0.084$\\pm$0.029 & 0.087$\\pm$0.021 & $<$[*1.075*]{} & 6.026$\\pm$0.130 & 94.0$\\pm$1.2 & $>$[*0.029*]{}\\\n& Q & C & 1.427$\\pm$0.134 & 1.360$\\pm$0.093 & 0.503$\\pm$0.034 & ... & ... & 2.228$\\pm$ 0.304\\\n& & J1 & 0.136$\\pm$0.042 & 0.094$\\pm$0.024 & 1.521$\\pm$0.383 & 2.632$\\pm$0.191 & 107.0$\\pm$4.2 & 0.023$\\pm$ 0.012\\\n& W & C & 0.691$\\pm$0.057 & 0.600$\\pm$0.037 & 0.443$\\pm$0.027 & ... & ... & 1.391$\\pm$ 0.173\\\n& D & C & 0.298$\\pm$0.046 & 0.253$\\pm$0.030 & 0.326$\\pm$0.039 & ... & ... & 1.107$\\pm$ 0.263\\\n2230+114 & K & C & 2.227$\\pm$0.097 & 2.119$\\pm$0.067 & 0.968$\\pm$0.031 & ... & ... & 0.795$\\pm$ 0.050\\\n& & J1 & 0.299$\\pm$0.056 & 0.189$\\pm$0.030 & 3.013$\\pm$0.480 & 5.372$\\pm$0.240 & 167.2$\\pm$2.6 & 0.011$\\pm$ 0.004\\\n& Q & C & 2.235$\\pm$0.213 & 1.995$\\pm$0.142 & 0.719$\\pm$0.051 & ... & ... & 1.447$\\pm$ 0.206\\\n& W & C & 1.618$\\pm$0.083 & 1.519$\\pm$0.057 & 0.260$\\pm$0.010 & ... & ... & 8.010$\\pm$ 0.600\\\n& D & C & 1.308$\\pm$0.171 & 1.078$\\pm$0.109 & 0.325$\\pm$0.033 & ... & ... & 4.144$\\pm$ 0.838\\\n& & J1 & 0.199$\\pm$0.020 & 0.190$\\pm$0.014 & 0.144$\\pm$0.011 & 0.761$\\pm$0.005 & 73.8$\\pm$0.4 & 3.212$\\pm$ 0.478\\\n& & J2 & 0.165$\\pm$0.064 & 0.170$\\pm$0.046 & $<$[*0.181*]{} & 1.046$\\pm$0.025 & 115.8$\\pm$1.3 & $>$[*1.677*]{}\\\n2251+158 & K & C & 5.924$\\pm$0.499 & 5.936$\\pm$0.353 & $<$[*0.236*]{} & ... & ... & $>$[*32.440*]{}\\\n& & J2 & 0.582$\\pm$0.100 & 0.485$\\pm$0.064 & 1.842$\\pm$0.244 & 3.856$\\pm$0.122 & -92.3$\\pm$1.8 & 0.052$\\pm$ 0.014\\\n& & J3 & 0.368$\\pm$0.161 & 0.388$\\pm$0.117 & $<$[*1.234*]{} & 7.690$\\pm$0.186 & -69.3$\\pm$1.4 & $>$[*0.074*]{}\\\n& & J4 & 0.249$\\pm$0.053 & 0.224$\\pm$0.036 & 1.458$\\pm$0.232 & 11.371$\\pm$0.116 & -58.6$\\pm$0.6 & 0.036$\\pm$ 0.011\\\n& Q & C & 8.868$\\pm$0.190 & 8.721$\\pm$0.133 & 0.268$\\pm$0.004 & ... & ... & 37.709$\\pm$ 1.152\\\n& & J1 & 0.555$\\pm$0.184 & 0.217$\\pm$0.067 & 2.128$\\pm$0.658 & 2.062$\\pm$0.329 & -120.1$\\pm$9.1 & 0.037$\\pm$ 0.023\\\n& W & C & 8.954$\\pm$0.424 & 8.073$\\pm$0.284 & 0.331$\\pm$0.012 & ... & ... & 24.961$\\pm$ 1.756\\\n& D & C & 6.124$\\pm$0.390 & 5.933$\\pm$0.271 & 0.127$\\pm$0.006 & ... & ... & 115.964$\\pm$10.610\\\n\n[^1]: http://sci.esa.int/integral/\n\n[^2]: http://agile.rm.iasf.cnr.it/\n\n[^3]: http://fermi.gsfc.nasa.gov/\n" ]

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[ "http://www.JewishWorldReview.com |\nSince the navy's May 31 takeover of the Turkish-Hamas flotilla, Prime Minister Binyamin Netanyahu and his advisers have deliberated around the clock about how to contend with the US-led international stampede against Israel. ", "But their ultimate decision to form an investigatory committee led by a retired Supreme Court justice and overseen by foreign observers indicates that they failed to recognize the nature of the international campaign facing us today.", "\n\nLed by US President Barack Obama, the West has cast its lot with Hamas. ", "It is not surprising that Obama is siding with Hamas. ", "His close associates are leading members of the pro-Hamas Free Gaza outfit. ", "Obama's friends, former Weather Underground terrorists Bernadine Dohrn and William Ayres participated in a Free Gaza trip to Egypt in January. ", "Their aim was to force the Egyptians to allow them into Gaza with 1,300 fellow Hamas supporters. ", "Their mission was led by Code Pink leader and Obama fund-raiser Jodie Evans. ", "Another leading member of Free Gaza is James Abourezk, a former US senator from South Dakota.", "\n\nAll of these people have open lines of communication not only to the Obama White House, but to Obama himself.", "\n\nObama has made his sympathy for the Muslim Brotherhood clear several times since entering office. ", "The Muslim Brotherhood's progeny include Hamas, al-Qaida and the Egyptian Islamic Jihad. ", "Last June, Obama infuriated the Egyptian government when he insisted on inviting leaders of the Muslim Brotherhood to attend his speech at Al Azhar University in Cairo. ", "His administration's decision to deport Hamas deserter and Israeli counterterror operative Mosab Hassan Yousef to the Palestinian Authority where he will be killed is the latest sign of its support for radical Islam.", "\n\nGiven Obama's attitude toward jihadists and the radical leftists who support them, his decision to support Hamas against Israel makes sense. ", "What is alarming however is how leaders of the free world are now all siding with Hamas. ", "That support has become ever more apparent since the Mossad's alleged killing of Hamas terror master Mahmoud al-Mabhouh at his hotel in Dubai in January.", "\n\nIn the aftermath of Mabhouh's death, both Britain and Australia joined the Dubai-initiated bandwagon in striking out against Israel. ", "Israel considers both countries allies, or at least friendly and has close intelligence ties with both. ", "Yet despite their close ties, Australia and Britain expelled Israeli diplomats who supposedly had either a hand in the alleged operation or who work for the Mossad.", "\n\nIt should be noted that neither country takes steps against outspoken terror supporters who call for Israel to be destroyed and call for the murder of individual Israelis.", "\n\nFor instance, in an interview last month with The Australian, Ali Kazak, the former PLO ambassador to Australia, effectively solicited the murder of The Jerusalem Post's Palestinian affairs correspondent Khaled Abu Toameh. ", "Kazak told the newspaper, \"Khaled Abu Toameh is a traitor.\"", "\n\nAllowing that many Palestinians have been murdered for such accusations, Kazak excused those extrajudicial murders saying, \"Traitors were also murdered by the French Resistance, in Europe; this happens everywhere.\"", "\n\nNot only did Australia not expel Kazak or open a criminal investigation against him, as a consequence of his smear campaign against Abu Toameh, several Australian government officials cancelled their scheduled meetings with him.", "\n\nAND OF course, this week we have the actions of Germany and Poland. ", "They are considered Israel's best friends in Europe, and yet acting on a German arrest warrant, Poland has arrested a suspected Mossad officer named Uri Brodsky for his alleged involvement in the alleged Mossad operation against Mabhouh. ", "Israel is now caught in a diplomatic disaster zone where its two closest allies — who again are only too happy to receive regular intelligence updates from the Mossad — are siding with Hamas against it.", "\n\nAnd then of course we have the EU's call for Israel to cancel its lawful blockade of the Gaza coast. ", "That is, the official position of the EU is that an Iranian proxy terrorist organization should be allowed to gain control over a Mediterranean port and through it, provide Iran with yet another venue from which it can launch attacks against Europe.", "\n\nFor their part, the Sunni Arabs are forced to go along with this. ", "The Egyptian regime considers the fact that the Muslim Brotherhood took over Gaza a threat to its very survival and has been assiduously sealing its border with Gaza for some time. ", "And yet, unable to be more anti-Hamas than the US, Australia and Europe, Mubarak is opening the border. ", "Arab League Secretary-General Amr Moussa's unprecedented visit to Gaza this week should be seen as a last ditch attempt by Egypt to convince Hamas to unify its ranks with Fatah. ", "Predictably, the ascendant Hamas refused his entreaties.", "\n\nAs for Fatah, it is hard not to feel sorry for its leader Mahmoud Abbas these days. ", "In what was supposed to be a triumphant visit to the White House, Abbas was forced to smile last week as Obama announced the US will provide $450 million in aid to his sworn enemies who three years ago ran him and his Fatah henchmen out of Gaza.", "\n\nSo too, Abbas is forced to cheer as Obama pressures Israel to give Hamas an outlet to the sea. ", "This will render it impossible for Fatah to ever unseat Hamas either by force or at the ballot box. ", "Hamas's international clout demonstrates to the Palestinians that jihad pays.", "\n\nTHERE ARE three plausible explanations for the West's decision to back Hamas. ", "All of them say something deeply disturbing about the state of the world. ", "The first plausible explanation is that the Americans and the rest of the West are simply naive. ", "They believe that by backing Hamas, they are advancing the cause of Middle East peace.", "\n\nIf this is in fact what the likes of Obama and his European and Australian counterparts think, apparently no one in the West is thinking very hard. ", "The fact is that by backing Hamas against Israel, they are backing Hamas against Fatah and they are backing Iran, Syria, Turkey, Hamas and Hizbullah against Egypt, Jordan and Saudi Arabia. ", "They are backing the most radical actors in the region — and arguably in the world — against states and regimes they have a shared strategic interest in strengthening.", "\n\nThere is absolutely no way this behavior advances the cause of peace.", "\n\nThe second plausible explanation is that the West's support for Hamas is motivated by hatred of Israel. ", "As Helen Thomas's recent remarks demonstrated, there is certainly a lot of that going around.", "\n\nThe final plausible explanation for the West's support for Hamas is that it has been led to believe that by acting as it is, it will buy itself immunity from attack by Hamas and its fellow members of the Iranian axis. ", "As former Italian president Francesco Cossiga first exposed in a letter to Corriere della Serra in August 2008, in the early 1970s Italian prime minister Aldo Moro signed a deal with Yasser Arafat that gave the PLO and its affiliated organizations the freedom to operate terror bases in Italy. ", "In exchange the Palestinians agreed to limit their attacks to Jewish and Israeli targets. ", "Italy maintained its allegiance to the deal — and to the PLO against Israel — even when Italian targets were hit.", "\n\nCossiga told the newspaper that the August 2, 1980 bombing at the Bologna train station — which Italy blamed on Italian fascists — was actually the work of George Habash's Popular Front for the Liberation of Palestine. ", "Eighty-five people were murdered in the attack, and still Italy maintained its agreement with the PLO to the point where it prosecuted and imprisoned the wrong people for the worst terrorist attack in its history.", "\n\nCossiga alleged that the deal is still in place today and that Italian forces in UNIFIL have expanded the deal to include Hamas's fellow Iranian proxy Hizbullah. ", "It isn't much of a stretch to consider the possibility that Italy and the rest of the Western powers have made a similar deal with Hamas. ", "And it is no stretch at all to believe that they will benefit from it as greatly as the Italian railroad passengers in Bologna did.", "\n\nTrue, no one has come out and admitted to supporting Hamas. ", "So too, no one has expressed anything by love for Israel and the Jewish people. ", "But the actions of the governments of the West tell a different tale. ", "Without one or more of the explanations above, it is hard to understand their current policies.", "\n\nSince the flotilla incident, Netanyahu and his ministers have held marathon deliberations on how to respond to US pressure to accept an international inquisition into the IDF's lawful enforcement of the legal blockade of the Gaza coast. ", "Their deliberations went on at the same time as Netanyahu and his envoys attempted to convince Obama to stop his mad rush to give Hamas an outlet to the sea and deny Israel even the most passive right of self-defense.", "\n\nIt remains to be seen if their decision to form an investigative panel with international \"observers\" was a wise move or yet another ill-advised concession to an unappeasable administration. ", "What is certain, however, is that it will not end the West's budding romance with Hamas.", "\n\nThe West's decision to side with Hamas is devastating. ", "But whatever the reasons for it, it is a fact of life. ", "It is Netanyahu's duty to swallow this bitter pill and devise a strategy to protect the country from their madness.", "\n\nEvery weekday JewishWorldReview.com publishes what many in Washington and in the media consider \"must reading.\" ", "Sign up for the daily JWR update. ", "It's free. ", "Just click here.", "\n\nInterested in a private Judaic studies instructor — for free? ", "Let us know by clicking here.", "\n\nJWR contributor Caroline B. Glick is the senior Middle East Fellow at the Center for Security Policy in Washington, DC and the deputy managing editor of The Jerusalem Post. ", "Comment by clicking here." ]

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[ "If you are new to the business world and yet have a strong ambition to succeed with your business concept, take a few steps back and invest some quality time into writing a startup business plan. ", "Without it, the chances for success are equal to zero. ", "Simply put, you can’t start in any industry if first, you don’t do deep analyses of the niches, the competition, and the market altogether. ", "If you do start without it, you will be crushed. ", "There is no easier way to say this, as it is the utter truth. ", "If you are interested a little bit more in the reasons why this is absolutely the rule, read on to find out.", "\n\nParts of the Startup Business Plan\n\nFirst and foremost, here are the parts of every business plan:\n\nExecutive summary: mission/vision/goals\n\nMarketing and sales strategy\n\nCompetition\n\nThe management team and personnel\n\nOperations\n\nFinances\n\nAll of these give an in-depth look at every segment of the business. ", "Determining your mission, vision and goals is the stepping stone for every business endeavour. ", "Secondly, making a strategy about the sales and marketing will bring you closer to the ideal clientele, the market trends and tactics which include pricing, distribution and promotion.", "\n\nThirdly, it is extremely important to put in writing who your management team will be, the personnel and all their duties and obligations so that you specifically know who is responsible for what.", "\n\nNext, the extensive analysis of the competition will give you the advantage of knowing your rivals’ strengths and weaknesses and use them to place yourself ahead in the game\n\nThe operation segment, on the other hand, will discuss your premises, production facilities and your management information systems as well as the IT technology you will use.", "\n\nFinally, the finances will reveal the details of the cash flow, the forecasted profit, losses and balance sheets.", "\n\nThese are the essential parts that your startup business plan should include. ", "But, what can you do with all of this information? ", "The point is that each and every segment should propose a problem and several ideas for a solution accordingly. ", "After all, the startup business plan is not only a layout of your business but valid and reliable documentation that can serve as a guide through hard times. ", "Therefore, the business plan is also as follows.", "\n\nA Solution Holder\n\nThe startup business plan offers solutions to forecasted problems. ", "Be it with the competition, the marketing strategy, the operational activities or the gains and losses, the startup business plan will have all the important information at any time that will be the basis of every future decision. ", "So, should a problem appear, the solution should be sought among those pages.", "\n\nA Step-by-step Guide\n\nThe business plan is your step-by-step guide through every process of the business endeavours. ", "This imposes the need for you to prepare the startup business plan as a multistep guidebook which will remind you whether every area of business is covered with alternatives and solutions.", "\n\nStrategic Focus\n\nThe business plan will give you a strategic focus on the things that are relevant and will show you how to distribute roles and responsibilities. ", "For example, have you chosen the right audience for your products/services? ", "Who will make sure that your customers are happy and satisfied?… ", "And so on.", "\n\nSet Priorities\n\nFinally, the business plan will help you prioritise the mess of starting a business. ", "It is always overwhelming to begin a concept especially if it is in a competitive niche. ", "And even if the nice is not competitive, you still need to prioritise things because you can’t do everything at the same time. ", "This way, with the plan, you will be able to keep track of the important things and make sure that you allocate your time accordingly to the importance of the tasks." ]

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[ "Built by Family, for Family\n\nKnowledge is Power\n\nKnowledge is power. ", "But a lack of knowledge would make you what? ", "Of that I am not really sure. ", "But any way we are trying to get our electrical poles installed and have run into some obstacles, namely more granite. ", "So because of this two of our four pole holes are rock holes. ", "This means they cost more because they have to drill through rock. ", "On one of them they also have to install an anchor into the rock, extra cost. ", "But once they are complete they should never go anywhere. ", "So what went from a 2-3 day job turned into about 10 days." ]

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[ "Q:\n\nRedirect loop on wp-admin or wp-login.php\n\nI put together a quick WordPress site locally using MAMP, then checked it into an SVN repo. ", "I then checked it out on to my development server.", "\nI didn't change anything except to run the search and replace tool script from Interconnectit to updated the URL of the site in the database on the server.", "\nInitially, I got a 500 server error. ", "Checking the logs, I discovered that this \"SoftException\" was because index.php was writeable by group - the permissions were 664. ", "No problem - a quick change of permissions to 644 sorted that. ", "So now the frontside was working.", "\nHowever, strangely, the admin side of the site did not work. ", "It just produced an endless redirect loop in all browsers.", "\nError 310 (net::ERR_TOO_MANY_REDIRECTS): There were too many redirects.", "\n\nNothing has changed since the local development version. ", "The htaccess file is just a standard WordPress one. ", "Nothing weird... still working fine locally.", "\nSo what's going on?", "\n\nA:\n\nFor whatever reason /wp-admin/ path causes a redirect loop, but /wp-admin/index.php does not. ", "As such, we can use .htaccess to redirect the /wp-admin/ path to /wp-admin/index.php by adding the following line to your .htaccess file after \"RewriteBase /\" line like this:\nRewriteBase /\nRewriteRule /wp-admin/ /wp-admin/index\\.php [L,P]\n\nIt worked for me like that.", "\nYou final .htaccess would probably look like this:\n# BEGIN WordPress\n<IfModule mod_rewrite.c>\nRewriteEngine On\nRewriteBase /\nRewriteRule /wp-admin/ /wp-admin/index\\.php [L,P]\nRewriteRule ^index\\.php$ - [L]\nRewriteCond %{REQUEST_FILENAME} !", "-f\nRewriteCond %{REQUEST_FILENAME} !", "-d\nRewriteRule . ", "/index.php [L]\n</IfModule>\n# END WordPress\n\nA:\n\nChecking the permissions of wp-login.php revealed that they too had somehow been set to 664 - the same permissions that caused index.php to fail and caused the 500 server error.", "\nI changed the permissions of wp-login.php to 644 and hey presto, the WordPress login page showed up. ", "\nBut on logging in, another redirect loop. ", "So, once again, looking at /wp-admin/index.php, the permissions were 664 rather than 644. ", "\nFixing them led to problems with the next files in line - the dashboard was a right mess. ", "One by one, changing from 664 to 644 corrected the issues (/wp-admin/load-scripts.php, /wp-admin/load-styles.php). ", "\nSo it became obvious that a recursive change of permissions was the only way to sort things out.", "\nMy UNIX isn't exactly top notch, but this appears to have worked (running from Mac OS X Terminal). ", "I ran it from the root directory of this WP install.", "\nfind . ", "-type f -perm 664 -print -exec chmod 644 {} \\;\n\nThere might be a better command, but I understand this to mean \"find all files with 664 permissions and change them to 644\".", "\nIt has fixed my problem.", "\n\nA:\n\nIf you're using Cloudflare you might want to try adding this to the TOP of your wp-config.php file:\ndefine('WP_SITEURL', 'https://www.example.com');\ndefine('WP_HOME', 'https://www.example.com');\ndefine('FORCE_SSL_ADMIN', true);\ndefine('FORCE_SSL_LOGIN', true);\nif(isset($_SERVER['HTTP_CF_VISITOR']) && strpos($_SERVER['HTTP_CF_VISITOR'], 'https')){\n $_SERVER['HTTPS']='on';\n}\n\nIt's important that you add it to the top of the wp-config.php file or you'll end up with \"Sorry, you are not allowed to access this page\" error messages.", "\nCredit: https://www.meltajon.com/dev/wordpress-wp-admin-redirect-loop-with-cloudflare-ssl\n\n" ]

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[ "// Copyright 2011 The Go Authors. ", "All rights reserved.", "\n// Use of this source code is governed by a BSD-style\n// license that can be found in the LICENSE file.", "\n\n// Package s2k implements the various OpenPGP string-to-key transforms as\n// specified in RFC 4800 section 3.7.1.", "\npackage s2k // import \"golang.org/x/crypto/openpgp/s2k\"\n\nimport (\n\t\"crypto\"\n\t\"hash\"\n\t\"io\"\n\t\"strconv\"\n\n\t\"golang.org/x/crypto/openpgp/errors\"\n)\n\n// Config collects configuration parameters for s2k key-stretching\n// transformatioms. ", "A nil *Config is valid and results in all default\n// values. ", "Currently, Config is used only by the Serialize function in\n// this package.", "\ntype Config struct {\n\t// Hash is the default hash function to be used. ", "If\n\t// nil, SHA1 is used.", "\n\tHash crypto.", "Hash\n\t// S2KCount is only used for symmetric encryption. ", "It\n\t// determines the strength of the passphrase stretching when\n\t// the said passphrase is hashed to produce a key. ", "S2KCount\n\t// should be between 1024 and 65011712, inclusive. ", "If Config\n\t// is nil or S2KCount is 0, the value 65536 used. ", "Not all\n\t// values in the above range can be represented. ", "S2KCount will\n\t// be rounded up to the next representable value if it cannot\n\t// be encoded exactly. ", "When set, it is strongly encrouraged to\n\t// use a value that is at least 65536. ", "See RFC 4880 Section\n\t// 3.7.1.3.", "\n\tS2KCount int\n}\n\nfunc (c *Config) hash() crypto.", "Hash {\n\tif c == nil || uint(c.", "Hash) == 0 {\n\t\t// SHA1 is the historical default in this package.", "\n\t\treturn crypto.", "SHA1\n\t}\n\n\treturn c.Hash\n}\n\nfunc (c *Config) encodedCount() uint8 {\n\tif c == nil || c.S2KCount == 0 {\n\t\treturn 96 // The common case. ", "Correspoding to 65536\n\t}\n\n\ti := c.S2KCount\n\tswitch {\n\t// Behave like GPG. ", "Should we make 65536 the lowest value used?", "\n\tcase i < 1024:\n\t\ti = 1024\n\tcase i > 65011712:\n\t\ti = 65011712\n\t}\n\n\treturn encodeCount(i)\n}\n\n// encodeCount converts an iterative \"count\" in the range 1024 to\n// 65011712, inclusive, to an encoded count. ", "The return value is the\n// octet that is actually stored in the GPG file. ", "encodeCount panics\n// if i is not in the above range (encodedCount above takes care to\n// pass i in the correct range). ", "See RFC 4880 Section 3.7.7.1.", "\nfunc encodeCount(i int) uint8 {\n\tif i < 1024 || i > 65011712 {\n\t\tpanic(\"count arg i outside the required range\")\n\t}\n\n\tfor encoded := 0; encoded < 256; encoded++ {\n\t\tcount := decodeCount(uint8(encoded))\n\t\tif count >= i {\n\t\t\treturn uint8(encoded)\n\t\t}\n\t}\n\n\treturn 255\n}\n\n// decodeCount returns the s2k mode 3 iterative \"count\" corresponding to\n// the encoded octet c.\nfunc decodeCount(c uint8) int {\n\treturn (16 + int(c&15)) << (uint32(c>>4) + 6)\n}\n\n// Simple writes to out the result of computing the Simple S2K function (RFC\n// 4880, section 3.7.1.1) using the given hash and input passphrase.", "\nfunc Simple(out []byte, h hash.", "Hash, in []byte) {\n\tSalted(out, h, in, nil)\n}\n\nvar zero [1]byte\n\n// Salted writes to out the result of computing the Salted S2K function (RFC\n// 4880, section 3.7.1.2) using the given hash, input passphrase and salt.", "\nfunc Salted(out []byte, h hash.", "Hash, in []byte, salt []byte) {\n\tdone := 0\n\tvar digest []byte\n\n\tfor i := 0; done < len(out); i++ {\n\t\th.Reset()\n\t\tfor j := 0; j < i; j++ {\n\t\t\th.Write(zero[:])\n\t\t}\n\t\th.Write(salt)\n\t\th.Write(in)\n\t\tdigest = h.Sum(digest[:0])\n\t\tn := copy(out[done:], digest)\n\t\tdone += n\n\t}\n}\n\n// Iterated writes to out the result of computing the Iterated and Salted S2K\n// function (RFC 4880, section 3.7.1.3) using the given hash, input passphrase,\n// salt and iteration count.", "\nfunc Iterated(out []byte, h hash.", "Hash, in []byte, salt []byte, count int) {\n\tcombined := make([]byte, len(in)+len(salt))\n\tcopy(combined, salt)\n\tcopy(combined[len(salt):], in)\n\n\tif count < len(combined) {\n\t\tcount = len(combined)\n\t}\n\n\tdone := 0\n\tvar digest []byte\n\tfor i := 0; done < len(out); i++ {\n\t\th.Reset()\n\t\tfor j := 0; j < i; j++ {\n\t\t\th.Write(zero[:])\n\t\t}\n\t\twritten := 0\n\t\tfor written < count {\n\t\t\tif written+len(combined) > count {\n\t\t\t\ttodo := count - written\n\t\t\t\th.Write(combined[:todo])\n\t\t\t\twritten = count\n\t\t\t} else {\n\t\t\t\th.Write(combined)\n\t\t\t\twritten += len(combined)\n\t\t\t}\n\t\t}\n\t\tdigest = h.Sum(digest[:0])\n\t\tn := copy(out[done:], digest)\n\t\tdone += n\n\t}\n}\n\n// Parse reads a binary specification for a string-to-key transformation from r\n// and returns a function which performs that transform.", "\nfunc Parse(r io.", "Reader) (f func(out, in []byte), err error) {\n\tvar buf [9]byte\n\n\t_, err = io.", "ReadFull(r, buf[:2])\n\tif err !", "= nil {\n\t\treturn\n\t}\n\n\thash, ok := HashIdToHash(buf[1])\n\tif !", "ok {\n\t\treturn nil, errors.", "UnsupportedError(\"hash for S2K function: \" + strconv.", "Itoa(int(buf[1])))\n\t}\n\tif !", "hash.", "Available() {\n\t\treturn nil, errors.", "UnsupportedError(\"hash not available: \" + strconv.", "Itoa(int(hash)))\n\t}\n\th := hash.", "New()\n\n\tswitch buf[0] {\n\tcase 0:\n\t\tf := func(out, in []byte) {\n\t\t\tSimple(out, h, in)\n\t\t}\n\t\treturn f, nil\n\tcase 1:\n\t\t_, err = io.", "ReadFull(r, buf[:8])\n\t\tif err !", "= nil {\n\t\t\treturn\n\t\t}\n\t\tf := func(out, in []byte) {\n\t\t\tSalted(out, h, in, buf[:8])\n\t\t}\n\t\treturn f, nil\n\tcase 3:\n\t\t_, err = io.", "ReadFull(r, buf[:9])\n\t\tif err !", "= nil {\n\t\t\treturn\n\t\t}\n\t\tcount := decodeCount(buf[8])\n\t\tf := func(out, in []byte) {\n\t\t\tIterated(out, h, in, buf[:8], count)\n\t\t}\n\t\treturn f, nil\n\t}\n\n\treturn nil, errors.", "UnsupportedError(\"S2K function\")\n}\n\n// Serialize salts and stretches the given passphrase and writes the\n// resulting key into key. ", "It also serializes an S2K descriptor to\n// w. The key stretching can be configured with c, which may be\n// nil. ", "In that case, sensible defaults will be used.", "\nfunc Serialize(w io.", "Writer, key []byte, rand io.", "Reader, passphrase []byte, c *Config) error {\n\tvar buf [11]byte\n\tbuf[0] = 3 /* iterated and salted */\n\tbuf[1], _ = HashToHashId(c.hash())\n\tsalt := buf[2:10]\n\tif _, err := io.", "ReadFull(rand, salt); err !", "= nil {\n\t\treturn err\n\t}\n\tencodedCount := c.encodedCount()\n\tcount := decodeCount(encodedCount)\n\tbuf[10] = encodedCount\n\tif _, err := w.Write(buf[:]); err !", "= nil {\n\t\treturn err\n\t}\n\n\tIterated(key, c.hash().New(), passphrase, salt, count)\n\treturn nil\n}\n\n// hashToHashIdMapping contains pairs relating OpenPGP's hash identifier with\n// Go's crypto.", "Hash type. ", "See RFC 4880, section 9.4.", "\nvar hashToHashIdMapping = []struct {\n\tid byte\n\thash crypto.", "Hash\n\tname string\n}{\n\t{1, crypto.", "MD5, \"MD5\"},\n\t{2, crypto.", "SHA1, \"SHA1\"},\n\t{3, crypto.", "RIPEMD160, \"RIPEMD160\"},\n\t{8, crypto.", "SHA256, \"SHA256\"},\n\t{9, crypto.", "SHA384, \"SHA384\"},\n\t{10, crypto.", "SHA512, \"SHA512\"},\n\t{11, crypto.", "SHA224, \"SHA224\"},\n}\n\n// HashIdToHash returns a crypto.", "Hash which corresponds to the given OpenPGP\n// hash id.\nfunc HashIdToHash(id byte) (h crypto.", "Hash, ok bool) {\n\tfor _, m := range hashToHashIdMapping {\n\t\tif m.id == id {\n\t\t\treturn m.hash, true\n\t\t}\n\t}\n\treturn 0, false\n}\n\n// HashIdToString returns the name of the hash function corresponding to the\n// given OpenPGP hash id.\nfunc HashIdToString(id byte) (name string, ok bool) {\n\tfor _, m := range hashToHashIdMapping {\n\t\tif m.id == id {\n\t\t\treturn m.name, true\n\t\t}\n\t}\n\n\treturn \"\", false\n}\n\n// HashIdToHash returns an OpenPGP hash id which corresponds the given Hash.", "\nfunc HashToHashId(h crypto.", "Hash) (id byte, ok bool) {\n\tfor _, m := range hashToHashIdMapping {\n\t\tif m.hash == h {\n\t\t\treturn m.id, true\n\t\t}\n\t}\n\treturn 0, false\n}\n" ]

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[ "Nava Bharathi Vidya Niketan High School\n\nNava Bharathi Vidya Niketan High School is located in Pragi, a town in the Ranga Reddy district of India.", "\n\nSee also\nEducation in India\nList of schools in India\n\nReferences\n\nExternal links \n\nCategory:High schools and secondary schools in Hyderabad, India\nCategory:1989 establishments in India\nCategory:Educational institutions established in 1989" ]

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[ "Ed. ", "note: Since publication of this article, Eric Hites aka Fat Guy Across America has reopened his GoFundMe campaign to accept donations. ", "He continues to request that followers donate to PayPal directly.", "\n\nConcerned folks from around the world have been pestering us pretty much non-stop since the GoFraudMe Facebook page was born to cover this Fat Guy Across America dude. ", "In case you don’t know, Eric Hites is — as he self-describes — a fat guy who wanted to win his wife back by biking across America.", "\n\nIn June of last year, Hites slapped up a GoFundMe page seeking $20k to support him in this journey.", "\n\nHere’s what he wrote:\n\n“All of my life I dreamt of having that one life-changing adventure that would set me on a course to achieve an extraordinary life. ", "Now I’m doing it, and I want you to join me! ", "I will be bicycling across America – traveling east coast to west coast — on a quest to rebuild my marriage and adopt a healthier lifestyle. ", "Throughout the trip, I plan to visit interesting locations and to meet up with some amazing people. ", "Along the way, I’ll be sharing all of the excitement, as well as the bumps in the road with my supporters through blogging and posting about my experience. ", "The road will have it ups and downs, but together we’ll get there.”", "\n\nSo far so good, right? ", "Well, maybe not.", "\n\nCritics of Fat Guy say he sure has a lot of time on his hands to delete comments from his Facebook page when he’s supposed to be out there biking. ", "And about that biking? ", "Yeah, he’s not really making it across America. ", "I mean, eventually.", "\n\nDr Phil grilled Fat Guy earlier this year and let’s just say it didn’t go well.", "\n\nAccording to Fat Guy, he started out at 567 pounds and is down to 480 pounds as of April 2016. ", "You’ll note that he claimed to have lost 60 pounds in the first two weeks of his journey.", "\n\nCritics say Fat Guy seems to eat a lot of junk food and laze around in motels quite a bit for someone who is supposedly on a cross-country journey to get healthy. ", "Some, like this random dude on Facebook, basically tell him he’s full of shit to his face (if virtually).", "\n\nOne of Eric’s supporters — who also happens to follow us on Facebook — had the following to say in defense of Hites’ troubled journey:\n\n“My view is he has put himself out there. ", "He updates. ", "He can take 10 years if he wants. ", "If people want to contribute they can. ", "He never has lied about the journey and his troubles. ", "Like I said not well planned out but it is his journey and if people are not happy do not follow him.”", "\n\nAnd that is certainly true, as he calls himself Fat Guy Across America not Fat Guy Across America in a Reasonable Amount of Time or Fat Guy Hustling Across America Quickly.", "\n\nNow, back to the topic at hand, which is not Fat Guy nor his excessively slow journey but GoFundMe. ", "In his final update to the Fat Guy GoFundMe page before closing it for donations, he cites harassment as his motivation for wrapping up the fundraiser.", "\n\nIs Fat Guy Across America a fraud? ", "As stated above, he is technically making his way across America, albeit slowly. ", "According to Strava, he’s logged 769.5 miles this year so far.", "\n\nIt’s entirely possible he’s using the money for cigarettes and Twinkies, but it’s also possible that this unemployed, unhealthy Fat Guy is spending it on Motel 6 rooms and sturdy bike seats. ", "Shit, it’s GoFundMe, he could be using the money for cocaine and deep fried banana and bacon sandwiches for all we know. ", "Isn’t that the entire point of GoFundMe?", "\n\nAny thoughts, feelings, experiences, and/or fond memories of Fat Guy welcome in the comments. ", "Please refrain from fat shaming as this is a safe space, you thin privilege shitlords! ", "Just kidding, do whatever the hell you want.", "\n\nShare this: Facebook\n\nLinkedIn\n\nReddit\n\nTwitter\n\nGoogle\n\n" ]

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[ "Memory for people and their actions: further evidence for an age-related associative deficit.", "\nThe associative deficit hypothesis (M. Naveh-Benjamin, 2000) attributes age-related memory deficits to the inability to encode and retrieve bound units of information. ", "The present experiment extended this deficit to a new form of stimuli, dynamic displays of people and their performance of everyday actions. ", "Older and younger adults viewed a series of brief video clips, each showing a different person performing a different action, and were tested over memory for individual people, individual actions, and the person-action combinations. ", "Older adults did exhibit an associative deficit, and this was related to an increased proportion of false alarms on the associative test." ]

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[ "Q:\n\nWhy there are hearts around my Pokémon?", "\n\nI was playing sapphire today as usual but when I sent my zigzagoon to battle I noticed that there are hearts flown around him when it just came out of poke ball not the usual animations of lines or dots. ", "Why is that?", "\n\nA:\n\nDifferent kinds of Poké Balls have different animations for when they pop open. ", "In your case, I believe it's either a Nest Ball or a Luxury Ball.", "\n\n" ]

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[ "Alegação da Universidade para proibir o estudo é que o tema seria “politicamente incorreto”.", "\n\nCerca de cinco anos atrás, o Dr. Miroslav Djordjevic, um dos maiores especialistas em cirurgia genital reconstrutiva, recebeu uma visita em sua clínica, em Belgrado, capital da Sérvia, de um homem que havia se arrependido da mudança de sexo.", "\n\nEle conta que foi a primeira vez que conheceu alguém que alegava “arrependimento” após a operação, mas nos meses seguintes foi procurado por outras seis pessoas que desejavam “reverter” as mudanças em seus corpos. ", "Apesar do alto custo desse tipo de procedimento, o número não parou de crescer desde então.", "\n\nCom 22 anos de experiência, Djordjevic realiza cerca de 100 cirurgias por ano, tanto no conhecido Hospital Mount Sinai, em Nova York, nos Estados Unidos, quanto em sua clínica sérvia. ", "Ele revela que as pessoas que o procuram buscando reverter a sua mudança de sexo, sofrem de altos níveis de depressão. ", "Muitos, inclusive dizem pensar em suicídio.", "\n\nEm entrevista ao jornal britânico Telegraph, o médico declarou:\n\nPode ser um verdadeiro desastre escutar essas histórias.", "\n\nO especialista também disse que a maioria dos seus colegas importa-se apenas com o dinheiro, não com os sentimentos de seus pacientes:\n\nDevemos impedir que isto aconteça. ", "Como comunidade médica, devemos ter regras muito claras: ninguém que pretende fazer esse tipo de cirurgia ou apenas ganhar dinheiro deveria ser autorizado a fazê-las.", "\n\nO Dr. Djordjevic também criticou a realização de tratamentos hormonais para mudança de sexo das crianças.", "\n\nEticamente, devemos ajudar qualquer pessoa no mundo, mesmo que seja a partir de três anos de idade, mas da melhor forma possível”, disse. “", "Se querem mudar a saúde geral com qualquer remédio, eu não apoio essa teoria.", "\n\nEstudos censurados\n\nEntrevistado pela BBC, o Dr. James Caspian, psicoterapeuta que atende transexuais, conta que estava decidido a fazer uma pesquisa sobre o “destransicionamento” após uma conversa com Djordjevic em 2014.", "\n\nPreocupado com a falta de pesquisas sobre o assunto, propôs a realização de um estudo pelo centro de estudo da Universidade Bath Spa, na Inglaterra.", "\n\nPorém, o projeto acabou sendo cancelado sob alegação que seria “politicamente incorreto”. ", "Posteriormente, descobriu que sua proposta tinha sido rechaçada pelo comitê de ética do centro com o qual ele colabora.", "\n\nEle explicou o motivo do cancelamento:\n\nSeu principal argumento é que isso poderia causar críticas à pesquisa nas redes sociais, e as críticas à pesquisa seriam críticas à Universidade. ", "Além disso, sublinharam que é melhor não ofender as pessoas.", "\n\nCaspian já havia compilado achados preliminares os quais apontavam que há cada vez mais jovens, especialmente mulheres, que se arrependem de ter realizado a mudança de sexo.", "\n\nMesmo sem verba da Universidade, quis continuar realizando o seu estudo, mas foi atacado por ativistas pelos diretos dos trans.", "\n\nO doutor acrescentou:\n\nEu acho que uma universidade existe para encorajar a discussão, a pesquisa e até mesmo discordar, talvez desafiando ideias que estão desatualizadas ou que não são realmente úteis.", "\n\nSeu objetivo era estudar casos de pessoas que haviam mudado de sexo e depois se arrependeram. ", "Um dos objetivos seria identificar o quanto isso crescendo, justamente porque não encontrou nenhuma pesquisa sobre o assunto.", "\n\nCaspian assegura que os estudos mais antigos nessa área estão desatualizados.", "\n\n“Esse campo mudou completamente nos últimos anos”, garante, reforçando que sua pesquisa era necessária “para ajudar as pessoas que podiam ter arrependimentos posteriores”.", "\n\nAdaptado da fonte Gospel Prime" ]

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[ "Integration of depth modules: stereopsis and texture.", "\nGlobal shape judgements were employed to examine the combination of stereopsis and shape-from-texture in the determination of three-dimensional shape. ", "Adding textural variations to stereograms increased perceived depth. ", "Thus, texture was not simply vetoed by the strong stereo cue. ", "In experiments where the depth specified by texture was incongruent with that specified by stereo, the data were well described by a weighted linear combination rule. ", "Although only a small weight was assigned to texture, this weight was somewhat greater at a farther viewing distance. ", "This could be a consequence of the decreased reliability of stereopsis at far viewing distances." ]

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[ "It took a little longer than we had hoped to iron out all the details, but we were glad to see the city come to terms last week with the private group Las Cruces Community Partners to build a downtown plaza.", "\n\nMembers of the City Council approved a $5.397 million agreement with Community Partners, which is headed by local developer Bob Pofahl, for the plaza. ", "That will cover the costs to purchase 1.362 acres of land now being used for the Bank of the West drive-up facility at the northeast corner of Griggs Avenue and Main Street, and to build the plaza.", "\n\nLas Cruces Community Partners will be responsible for designing and building the civic plaza. ", "City Manager Robert Garza said payments to that group will be made in phases, as work on the plaza progresses, and the final price tag can not exceed $5,397 million. ", "The design is expected to include benches, grassed areas, trees, a covered outdoor stage, and some type of water fountain or water feature.", "\n\nGarza explained previously that there are advantages to having a public-private partnership for projects such as these. ", "For example, the private group can contract for services without going through the more burdensome request for proposals process required in the city,\n\nFunding for the plaza will come from the Tax Increment Development District, an innovative initiative passed several years ago by the state Legislature to allow targeted development in specific areas. ", "It allows local governments to take all taxes levied within the district — including taxes that would normally go to the state — and keep them in the district. ", "For Las Cruces, the TIDD provided the perfect vehicle to bolster downtown redevelopment efforts that had been lagging for years.", "\n\nThe city considered several proposals for its first project with the TIDD money, but settled on the plaza following a series of community meetings when residents made it clear a plaza was the top priority.", "\n\nWe agree with that decision.", "\n\nWhile much needs to be done downtown, the first step should be a place to come together as a community, and where multiple events can be held. ", "We have no doubt that once such a gathering place is built, it will attract further development and revitalization around the plaza.", "\n\n“The city has never really had that community gathering place,” Garza said. “", "This is a very exciting time, a very defining point for our downtown.”", "\n\nIt is expected to take about 18 months to complete work on the plaza. ", "That seems like a long time off until you consider the city has been working on this for some 25 years.", "\n\nWe eagerly look forward to the day that our plaza becomes the heart of our downtown, just as plazas in Mesilla, Santa Fe and elsewhere are now.", "\n\nLAS CRUCES >> Fifteen years after city officials began the first discussions and negotiations for a civic plaza in downtown Las Cruces, the venue took a major step toward becoming a reality.", "\n\nOn Tuesday, Las Cruces’ Tax Increment Development District board of commissioners — which consists of the seven-member Las Cruces City Council — met in closed session, then publicly voted to unanimously approve a $5.397 million purchase of 1.362 acres of property at the northeast corner of Griggs Avenue and Main Street. ", "It will become a civic plaza by March 2016.", "\n\n“Do it! ", "This ‘city’ needs to start looking like a city,” said Mark D. Nevarez, in a post on the Las Cruces Sun-News’ Facebook page.", "\n\nThe money to purchase the property, which has been a drive-up motor bank facility for more than 25 years, will come from taxes collected through the city’s downtown TIDD. ", "The land will be purchased from developer Las Cruces Community Partners, a nonprofit organization of business owners formed to serve downtown stakeholders, building owners and businesses headed by Bob Pofhal.", "\n\nDevelopment of a civic plaza has been a focal point of downtown revitalization, from city leaders and downtown business owners, for more than 10 years.", "\n\n“Ultimately, the city is going to move forward with a key element of downtown revitalization and we’re excited about that,” said Andy Hume, senior planner for the city of Las Cruces.", "\n\nWilliam “Rusty” Babington, an assistant city attorney, said the contract between the city and Las Cruces Community Partners will be a performance-based agreement.", "\n\n“At the end of 18 months we (the city) are going to have a turnkey plaza,” Babington said.", "\n\nCity Manager Robert Garza said Las Cruces Community Partners will be responsible for designing and building the civic plaza and will be paid in phases as it meets benchmarks in the construction of the plaza. ", "The plaza will be an outdoor gathering place for the community. ", "Anticipated conceptual plans include benches, grassed areas, trees, a covered outdoor stage, and some type of water fountain or water feature.", "\n\n“It’s very exciting to see it coming to fruition,” said Ceil Levatino, TIDD board commissioner.", "\n\nPerhaps Councilor Greg Smith best summed up many of the emotions Las Crucens have felt about a civic plaza.", "\n\n“It has been a dream, (and) a frustration,” said Smith, referring to the ups and downs, and time it has taken for a civic plaza to be developed. “", "But this community will definitely benefit from it. ", "It will be an asset, it will be a destination for the city.”", "\n\nMayor and TIDD board chairman, Ken Miyagishima, and Garza recognized the years of efforts by numerous people to reach this milestone.", "\n\n“This is a defining moment of downtown revitalization,” Miyagishima said. “", "It’s going to be fun, it’s going to be exciting.”", "\n\nIt was Garza, who was then public works director for the city of Las Cruces, who began negotiations with Bank of the West in 1999 to purchase the property that will become the city’s civic plaza. ", "The negotiations took several years, and stalled when the then City Council could not agree on a purchase price for the property.", "\n\nHowever, Garza said he felt quiet satisfaction Tuesday when the TIDD board finally agreed on a purchase price.", "\n\n“I’m excited about it,” Garza said. “", "I expect that as I look back on it, the negotiations I was involved in will likely be one of those things that’s going to be a substantial part of my career with the city. ", "The city has never really had that community gathering place. ", "This is a very exciting time, a very defining point for our downtown.”", "\n\nNational renowned real estate research firm, John Burns Real Estate Consulting, has ranked the top 25 housing amenities by generation based on feedback from more than 20,000 home shoppers. ", "This research confirms LCCP’s philosophy that one key to reviving downtown Las Cruces is to bring top amenities and attractions.", "\n\nLAS CRUCES — Las Cruces businessman Bob Pofahl has teamed up with the owner of the former Doña Ana County Courthouse in an effort to remake the downtown landmark into a five-star hotel, conference center and complex with restaurants and boutiques, he said.", "\n“The vision for the hotel is to create something similar to La Fonda or La Posada in Santa Fe or the Hotel Parq Central in Albuquerque, where the building’s history is preserved during the redevelopment progress,” said Pofahl of his plans with owner John Hoffman of El Paso.", "\n\nPofahl, managing partner for Las Cruces Community Partners LLC, is no stranger to re-imagining large projects. ", "He also is working with investors to redevelop the former Las Cruces Country Club property into a medical campus complete with a hospital and mixed use development.", "\n\nPofahl said the $20 million to $30 million courthouse project could be a major boost to downtown Las Cruces revitalization efforts.", "\n\nEmpty since 2008, when county government moved into new facilities on Motel Boulevard, the courthouse retains its designation on the state’s historic registry. ", "Construction of the building began in 1936, and it served as an active public building for 70 years.", "\n\nIn 2008, Hoffman bought the building at 251 W. Amador Ave., ", "which included the former Doña Ana County jail, for $1.5 million. ", "There were plans to renovate the building into apartments and office space. ", "While some demolition and restoration work was done, the building has never been fully restored.", "\n\nPofahl said Hoffman has “done environmental mitigation on the entire structure, as well as adding a new roof.” ", "Pofahl’s investment group plans to hire architect Stefanos Polyzoides of Moule & Polyzoides of Pasadena, Calif., to supervise the project, he said. “", "And LCCP is in discussions with LaTour Signature Hotels by ResortCom International of San Diego, Calif., as the operator for the hotel and conference center.”", "\n\nHe said talks with investors are ongoing “as we finalize marketing plans, complete studies and continue with preliminary designs and planning.", "\nEdie Henry, of Las Cruces looks over the large chandliers resting on the floor of the Doña Ana County Courthouse on Saturday during the 2014 Casas de Antaño (Houses of Yesteryear) Tour. ", "During the tour, plans were announced to renovate the courthouse into a business complex with a hotel and conference center. (", "Robin Zielinski – Sun-News)\n”\nFuture plan\n\nPofahl and Hoffman first made their announcement public Saturday during a tour of historic properties hosted by the Mesilla Valley Preservation Inc.\n\n“Plans call for the restoration of the existing courthouse as a conference center with several restaurants. ", "The addition of approximately 70 rooms on the west side of building will maintain the current architecture of the courthouse,” according to Pofahl and Hoffman. “", "We’re beginning a process that could take two or three years. ", "When you’re renovating a building like this, you have only one chance to get it right,” said Pofahl.", "\n\n“Public spaces will feature artifacts and exhibits of local history. ", "Rooms and public spaces will also feature photos, art and artifacts about the history of the building, and we would like the name to reflect the history, something like the Courthouse Hotel and Conference Center.”", "\n\nReaction\n\n“A downtown hotel is definitely needed,” said city councilor Miguel Silva, whose district includes the former courthouse. “", "It would be nice if some longer-term housing could be incorporated, too. ", "I’ve heard about some of the plans, but not about the addition of 70 rooms. ", "I thought of La Fonda in Santa Fe and a hotel in Taos when I first heard about (renovation) plans. ", "The ideas have potential.”", "\n\n“It’s extremely important for us to have a hotel downtown,” said Carrie La Tour, executive director of Downtown Las Cruces Partnership, a nonprofit program not connected to Pofahl’s investment group.", "\n\n“We’re very happy that this is starting to take shape,” she said.", "\n\n“It was always in the downtown plan to have a hotel or a boutique hotel,” said Heather Pollard, president of the nonprofit Amador Foundation, which is restoring the old Amador Hotel, just across the street from the courthouse, as a museum and a multiuse community gathering site. “", "To have it in a historic building is just a plus because it will be an economic driver for tourism. ", "And if we can partner with the Amador to have dining and a bar and cocktails at the Amador, it’s a win-win for the entire downtown revitalization,” Pollard said.", "\n\nPlans for the proposed 70-room addition should be ready to submit for approval soon, Pofahl said.", "\n\nhe Pueblo Revival courthouse was built with $150,000 in municipal bonds and $100,000 from a Depression-era Works Progress Administration grant. ", "The 37,000-square-foot building was dedicated on Feb. 22, 1938, and was designed by architect Percy McGhee, a protégé of renowned architect Henry Trost. ", "McGhee was also the architect for the first Thomas Branigan Library, now the Branigan Cultural Center.", "\n\nThroughout its history, the building has been lauded for its pleasing design, according to Las Cruces historian Christopher Schurtz, who wrote in the 2014 Casas de Antaña tour guide that famed war correspondent Ernie Pyle was a fan of the courthouse.", "\n\n“Pyle was critical of ugly government buildings, but wrote the Doña Ana County Courthouse had ‘thrown off the old square monstrosity of a courthouse and built something that didn’t look like a courthouse … you might take it for a fine private mansion.’ ", "In its early days, especially, when the old acequia wound visibly across the property, the site was noted for its fine landscaping, and its modest, manicured law, trees and surrounding shrubbery,” Schurtz wrote.", "\n\nBy S. Derrickson Moore\nOriginally published in the Las Cruces Sun News\n\nLAS CRUCES >> Hundreds turned out to see some of the Mesilla Valley’s most beloved old buildings during Saturday’s 2014 Casas de Antaño (Houses of Yesteryear) Tour\n\n“Preservation in Progress” was the theme of the fourth annual Mesilla Valley Preservation, Inc. tour, and sites ranged from a nearly restored church to the crumbling adobe walls of a mid-19th century home and massive renovation projects just entering the planning stage.", "\n\nFor Martin Amador Campbell, the tour was a trip down a vivid memory lane.", "\n\n“I was born in the Amador Hotel. ", "My great grandfather had a general store right over there across the street, and I used to visit in this house when I was a child,” he said, gesturing at the scaffolding surrounding the Nestor Armijo house. ", "150 E. Lohman Ave. ", "The building, currently owned by the Las Cruces Chamber of Commerce, dates to 1867, and offered visitors a chance to see large-scale, adobe stabilization work in progress.", "\n\n“My family owned the Amador Hotel, and I’d like to see it used more for public gatherings and meetings again. ", "I’m very happy to see the preservation efforts here,” Campbell said.", "\n\nMary Smith, of Phoenix, Ariz., who greeted visitors at the clubhouse of the old Las Cruces Country Club, 2700 N. Main St., also has some family ties to sites on this year’s tour.", "\n\n“My great uncle was Henry Trost and this was a Trost & Trost building. ", "We’ve been looking at the family history and identifying over 600 Trost & Trost buildings in Arizona, New Mexico and east Texas. ", "The firm did many styles in addition to Pueblo Revival: Greek Revival, Classical Revival, Mission, Prairie and more. ", "It’s possible we’ll discover more Trost & Trost buildings in this area,” Smith said.", "\n\n“The tour features buildings newly discovered and proven by MVP to have been designed by Trost & Trost, including the Las Cruces County Club clubhouse in Las Cruces. ", "The Mesilla Park School (now the Papen Center), 304 Bell Ave., ", "on this year’s tour, is also a Trost & Trost building. ", "They were premier architects of the Southwest,” said MVP’s founder Eric Liefeld.", "\n\nVisitors saw a lot of potential in the old Doña Ana County Courthouse, 251 W. Amador Ave., ", "as they toured a large, recently revealed room that was an original courtroom that had been filled in for other uses by the county. ", "Elegantly painted beams and intricate carved woodwork attracted admirers.", "\n\n“I’d love to see this turned into apartments. ", "It would be the kind of place I’d like to be, if I could afford to live here,” said Donny Prosise, of Las Cruces.", "\n\n“It could be a beautiful bed and breakfast, or maybe a complex with offices and restaurants and boutiques on the first floor,” said Trudy Cooper, of Las Cruces.", "\n\n“Our goal is to restore it as a hotel. ", "We think this is the most iconic historical building in Southern New Mexico and we hope it ignites everybody to see what you can do with historic buildings,” said Bob Pofahl, a developer who is working with the building’s owner, John Hoffman, to restore and repurpose the old Doña Ana County Courthouse.", "\n\n“We’re beginning a planning process that could take two or three years. ", "When you’re renovating a building like this, you have only one chance to get it right,” Pofahl said.", "\n\nVolunteers from the nonprofit Amador Foundation showed everything from beautifully restored, fully-furnished rooms to areas gutted to bare bones of old wooden wall frames and original adobe bricks. ", "The goal is to give the old hotel and former government building a new life as a museum and community gathering place.", "\n\nAfter seeing buildings in several stages of renovation, Linda Jacobs, of Las Cruces, said it was a pleasure to visit the nearly-completed Phillips Chapel CME Church at 638 N. Tornillo St.\n\n“We’re waiting for the creation of doors with nearly 100-year-old wood from Yukon Territory,” said Beth O’Leary, who has worked on recent renovation projects for the church.", "\n\nClarence Fielder, church elder and a grandchild of the church’s founders, was on hand to talk about the oldest existing African American Church in New Mexico, now on the New Mexico State Register of Cultural Properties and the National Register of Historic Places.", "\n\nHe’s pleased that the site has continued to be a functioning church since 2003, when Fielder, an NMSU emeritus history professor, began working with Terry Moody, then an NMSU graduate student, on restoration projects.", "\n\n“Services have continued throughout the process, even if it was just the minister and one parishioner,” Fielder said.", "\n\nOrganizers of the event estimated that more than 500 showed up for the tour.", "\n\nTour proceeds benefit programs of the nonprofit Mesilla Valley Preservation, Inc., which is “dedicated to preserving the architectural legacy of the Mesilla Valley in Southern New Mexico and to preserving the future of our past,” according to the group’s mission statement.”", "\n\nThrough workshops, tours, a website and a variety of educational and training efforts, the group focuses on “preservation techniques, traditional construction technology, local architectural history and the history and culture of southern New Mexico,” Liefeld said.", "\n\nFor information about the group and its tours, seminars and projects, visit mvpres.org." ]

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[ "Q:\n\nHow does my Site look in other countries\n\nI just made some changes to my website, it will display different greeting text for different continents, I have used Google's API to get location of the user\nregion = google.loader.ClientLocation.address.region;\ncountry = google.loader.ClientLocation.address.country;\ncountrycode = google.loader.", "ClientLocation.address.country_code;\n\nBut now i want to test this, so is there any way that i can access my site with the IP of another continent or country, or any other solution for this.", "\n\nA:\n\nI've built a tool that you might find useful, called GeoPeeker. ", "In my own testing I found proxies to be unreliable, so I designed GeoPeeker to use actual servers that render a site and provide DNS information from various remote locations. ", "It's handy for troubleshooting CDN and DNS issues.", "\nIt's also free to use and there are no ads.", "\n\nA:\n\nYou could use an online proxy service, located in the country you want to test for. ", "A list of free online proxies can be found at http://proxy.org/.\n\n" ]

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[ "Prognostic factors for persistent pain after a first episode of nonspecific idiopathic, non-traumatic neck pain: A systematic review.", "\nPrognosis of acute idiopathic neck pain is poor. ", "An overview of modifiable and non-modifiable prognostic factors for the development of chronic musculoskeletal neck pain after an episode of idiopathic, non-traumatic neck pain is needed. ", "Identify prognostic factors for pain intensity and perceived non-recovery at three, six and 12 months after a first episode of idiopathic, non-traumatic neck pain. ", "Systematic review METHODS: Systematic literature search up to October 21, 2017 for prospective prognostic studies with main outcomes perceived non-recovery and pain intensity. ", "The QUIPS was used for quality assessment. ", "Out of 2737 screened articles six prospective studies with high-risk-of-bias were identified, analyzing 47 and 43 factors for the outcome variables 'pain intensity' and 'perceived non-recovery', respectively. ", "Based on univariate- and multivariate analyses we found moderate evidence for 'age> 40 years' and 'concomitant back pain' to be prognostic for 'pain intensity'. ", "For the outcome 'perceived non-recovery' at 12 months, we found moderate evidence for both 'a previous period of neck pain' and 'accompanying headache' as prognostic variables for persistent pain, based on univariate analysis. ", "No prognostic factor was found which was retained in more than one multivariate analysis for the outcome variable 'perceived non-recovery'. ", "However, the quality of the evidence for these prognostic factors was low to very low. ", "This review identifies prognostic factors for neck pain, of which only a few are modifiable. ", "Further research is needed before drawing definite conclusions about the prognostic value of these factors." ]

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[ "---\nabstract: 'We consider a model for random walks on random environments (RWRE) with random subset of ${{\\mathbb{Z}}}^d$ as the vertices, and uniform transition probabilities on $2d$ points (two “coordinate nearest points” in each of the $d$ coordinate directions). ", "We prove that the velocity of such random walks is almost surely $0$, and give partial characterization of transience and recurrence in the different dimensions. ", "Finally we prove Central Limit Theorem (CLT) for such random walks, under a condition on the distance between coordinate nearest points.'", "\nauthor:\n- Ron Rosenthal\nbibliography:\n- 'pointproc.bib'\ntitle: Random Walk on Discrete Point Processes\n---\n\nIntroduction\n============\n\nBackground\n----------\n\n$~$\\\nRandom walk on random environments is the object of intensive mathematical research for more then 3 decades. ", "It deals with models from condensed matter physics, physical chemistry, and many other fields of research. ", "The common subject of all models is the investigation of movement of particles in an inhomogeneous media. ", "It turnes out that the randomness of the media (i.e. the environment) is responsible for some unexpected results, especially in large scale behavior. ", "In the general case, the random walk takes place in a countable graph $(V,E)$, but the most investigated models deals with the graph of the $d$-dimensional integer lattice, (i.e. $V={{\\mathbb{Z}}}^d$). ", "For some of the results on those models see [@Ze03], [@Sz00], [@Hu96] and [@Re05]. ", "The definition of RWRE involves two steps: First the environment is randomly chosen by some given probability, then the random walk, which takes place on this given fixed environment, is a Markov chain with transition probabilities that depend on the environment. ", "We note that the environment is kept fixed and does not evolve during the random walk, and that the random walk, given an environment, is not necessarily reversible. ", "The questions on RWRE come in two major types: quenched, in which the walk is distributed according to a given typical environment, and annealed, in which the distribution of the walk is taken according to an average on the environments. ", "The two main differences between the quenched and the annealed are: First the quenched is Markovian, while the annealed distribution is usually not. ", "Second, in most of the models we assume some kind of translation invariance on the environments and therefore annealed is usually translation invariance while quenched is not. ", "In contrast to most of the models for RWRE on ${{\\mathbb{Z}}}^d$, this work deals with non nearest neighbor random walks. ", "The subject of non nearest neighbor random walks has not been systematically studied. ", "For results on long range percolation see [@Be01]. ", "For literature on the subject in the one dimensional case see [@BG08],[@Br02], [@CS09]. ", "For some results on bounded non nearest neighbors see [@Ke84]. ", "For some results that are valid in that general case see [@Va02] and [@caputo2009invariance]. ", "For recurrence and transience criteria for random walks on random point processes, with transition probabilities between every two points proportional to their distance, see [@CFG8]. ", "Our model also has the property that the random walk is reversible. ", "For some results in this topic see [@BBHK], [@BP07], [@MP07] and [@SS09].", "\n\nThe Model\n---------\n\n$~$\\\nLet ${{\\mathbb{Z}}}^d$ be the $d$-dimensional lattice of integers. ", "We define ${{\\Omega}}=\\{0,1\\}^{{{\\mathbb{Z}}}^d}$ and $\\mathfrak{B}$ the Borel ${{\\sigma}}$-algebra (with respect to the product topology) on ${{\\Omega}}$. Let $Q$ be a probability measure on ${{\\Omega}}$. We assume the following about $Q$:\n\n$~$\\\n\\[Assumptions\\]\n\n1. ", " $Q$ is stationary and ergodic with respect to each of $\\{{{\\theta}}_{e_i}\\}_{i=1}^{d}$, where $e_i$ is the $i^{\\mbox{th}}$ principal axes and for $x\\in{{\\mathbb{Z}}}^d$ we define ${{\\theta}}_x:{{\\Omega}}\\rightarrow{{\\Omega}}$ as the shift in direction $x$, i.e for every $y\\in{{\\mathbb{Z}}}^d$ and every ${{\\omega}}\\in{{\\Omega}}$ we have ${{\\theta}}_{x}({{\\omega}})(y)={{\\omega}}(x+y)$.\\\n\n2. ", " $Q({{\\mathcal{P}}}({{\\omega}}) = \\emptyset)<1$, where $\\mathcal{P}({{\\omega}})=\\{x\\in{{\\mathbb{Z}}}^d:{{\\omega}}(x)=1\\}$.\n\nWe denote by ${{\\mathcal{E}}}=\\{\\pm e_i\\}_{i=1}^d$ the set of $2d$ points in ${{\\mathbb{Z}}}^d$ with length $1$.\n\nLet ${{\\Omega}}_0=\\{{{\\omega}}\\in{{\\Omega}}:{{\\omega}}(0)=1\\}$, it follows from assumption \\[Assumptions\\] that $Q({{\\Omega}}_0)>0$. We can therefore define the probability $P$ on ${{\\Omega}}_0$ as the conditional probability on ${{\\Omega}}_0$ of $Q$, i.e.: $$P(B)=Q(B|{{\\Omega}}_0)=\\frac{Q(B\\cap {{\\Omega}}_0)}{Q({{\\Omega}}_0)}~~~~~\\forall\nB\\in\\mathfrak{B}. ", "\\label{P_definition}$$ We denote by ${{\\mathbb{E}}}_Q$ and ${{\\mathbb{E}}}_P$ the expectation with respect to $Q$ and $P$ respectively.\\\n\nGiven ${{\\omega}}\\in{{\\Omega}}$ and $v\\in{{\\mathcal{P}}}({{\\omega}})$, for every vector $e\\in{{\\mathcal{E}}}$ there exist $Q$ almost surely infinitely many $k\\in{{\\mathbb{N}}}$ such that $v+ke\\in{{\\mathcal{P}}}({{\\omega}})$. \\[The\\_model\\_claim\\]\n\nGiven ${{\\omega}}$,$v$ and a vector $e$ as above, since ${{\\theta}}_e$ is measure preserving and ergodic with respect to $Q$, if we define ${{\\Omega}}_v=\\{{{\\omega}}\\in{{\\Omega}}:v\\in{{\\mathcal{P}}}({{\\omega}})\\}$ then $\\mathbbm{1}_{{{\\Omega}}_v}\\in\nL^1({{\\Omega}},\\mathfrak{B},Q)$, and therefore by Birkhoff’s Ergodic Theorem $$\\lim_{n\\rightarrow\\infty}\\frac{1}{n}\\sum_{k=0}^{n-1}{{{\\theta}}_e^k\\mathbbm{1}_{{{\\Omega}}_v}}={{\\mathbb{E}}}_Q(\\mathbbm{1}_{{{\\Omega}}_v})=Q({{\\Omega}}_v)=Q({{\\Omega}}_0)>0~~~Q~a.s.$$ Consequently, there $Q$ almost surely exist infinitely many integers such that ${{\\theta}}_e^k\\mathbbm{1}_{A_v}=1$, and therefore infinitely many $k\\in{{\\mathbb{N}}}$ such that $v+ke\\in{{\\mathcal{P}}}({{\\omega}})$.\n\nWe define for every $v\\in{{\\mathbb{Z}}}^d$ the set $N_v({{\\omega}})$ of the $2d$ “coordinate nearest neighbors” in ${{\\omega}}$, one for each direction. ", "By Claim \\[The\\_model\\_claim\\] $N_v({{\\omega}})$ is $Q$ almost surely a set of $2d$ points in ${{\\mathbb{Z}}}^d$.\\\n\n\\[fig:fig1\\]\n\nWe can now define a random walk for $P$-almost every ${{\\omega}}\\in {{\\Omega}}_0$ (on the space $(({{\\mathbb{Z}}}^d)^{{\\mathbb{N}}},\\mathcal{G},P_{{\\omega}})$, where $\\mathcal{G}$ is the ${{\\sigma}}$-algebra generated by cylinder functions) as the Markov chain taking values in ${{\\mathcal{P}}}({{\\omega}})$ with initial condition $$P_{{\\omega}}(X_0=0)=1, \\label{inital_condition}$$ and transition probability $$P_{{\\omega}}(X_{n+1}=u|X_n=v)=\\left\\{\n\\begin{array}{cc}\n0&~~~u\\notin N_v({{\\omega}}) \\\\\n\\frac{1}{2d}&~~~u\\in N_v({{\\omega}}) \\\\\n\\end{array}\n\\right. ,", "\\label{transition_probability}$$ which will be called the quenched law of the random walk. ", "We denote the corresponding expectation by $E_{{\\omega}}$.\n\nFinally, since for each $G\\in\\mathcal{G}$, the map $${{\\omega}}\\mapsto P_{{\\omega}}(G),$$ is $\\mathcal{B}$ measurable, we may define the probability measure $\\bold{P}=P\\otimes P_{{\\omega}}$ on $({{\\Omega}}_0\\times({{\\mathbb{Z}}}^d)^{{\\mathbb{N}}},\\mathcal{B}\\times\\mathcal{G})$ by $$\\bold{P}(B\\times G)=\\int_{B}{P_{{\\omega}}(G)P(d{{\\omega}})},~~~~\\forall B\\in\\mathfrak{B},~~\\forall G\\in\\mathcal{G}.$$ The marginal of $\\bf{P}$ on $({{\\mathbb{Z}}}^d)^{{\\mathbb{N}}}$, denoted by ${{\\mathbb{P}}}$, is called the annealed law of the random walk $\\{X_n\\}_{n=0}^\\infty$. We denote by ${{\\mathbb{E}}}$ the expectation with respect to ${{\\mathbb{P}}}$.\n\nWe will need one more definition:\n\nFor every $e\\in{{\\mathcal{E}}}^d$ we define $f_e:{{\\Omega}}\\rightarrow{{\\mathbb{N}}}^+$ by $$f_e({{\\omega}})=\\min\\{k>0:{{\\theta}}_e^k({{\\omega}})(0)={{\\omega}}(ke)=1\\}.$$ \\[f\\_e\\_defn\\]\n\nIn order to prove high dimensional Central Limit Theorem we will assume in addition to assumption \\[Assumptions\\] the following:\n\n$~$\\\n(3) There exists ${{\\epsilon}}_0>0$ such that for every coordinate direction $e\\in{{\\mathcal{E}}}$, $E_P(f_e^{2+{{\\epsilon}}_0})<\\infty$. \\[assumption3\\]\\\n\nMain Results\n------------\n\n$~$\\\nOur main goal is to characterize these kind of random walks on random environments. ", "The characterization is given by the following theorems:\\\n(1) Law of Large Numbers - For $P$ almost every ${{\\omega}}\\in{{\\Omega}}_0$, the limiting velocity of the random walk exists and equals zero. ", "More precisely:\n\nDefine the event $$A=\\left\\{\\lim_{n\\rightarrow\\infty}{\\frac{X_n}{n}}=0\\right\\}.$$ Then ${{\\mathbb{P}}}(A)=1$. \\[LLN\\]\n\n\\(2) Recurrence Transience Classification - We give a partial classification of recurrence transience for the random walk on a discrete point process. ", "The precise statements are:\n\nThe one dimensional random walk on a discrete point process is ${{\\mathbb{P}}}$-almost surely recurrent. ", "\\[tran\\_recu1\\]\n\nLet $({{\\Omega}},{{\\mathfrak{B}}},P)$ be a two dimensional discrete point process and assume there exists a constant $C>0$ such that $$\\sum_{k=N}^{\\infty}{\\frac{k\\cdot\nP(f_{e_i}=k)}{{{\\mathbb{E}}}(f_{e_i})}}\\leq\\frac{C}{N}~~~\\forall\ni\\in\\{1,2\\}~~\\forall N\\in{{\\mathbb{N}}}. ", "\\label{Cauchy_tail_ass}$$ which in particular holds, whenever $f_{e_i}$ has a second moment for $i\\in\\{1,2\\}$. Then the random walk is ${{\\mathbb{P}}}$ almost surely recurrent.\\[tran\\_recu2\\]\n\nLet $({{\\Omega}},{{\\mathfrak{B}}},P)$ be a d-dimensional discrete point process with $d\\geq 3$ then the random walk is ${{\\mathbb{P}}}$ almost surely transient.\\[tran\\_recu3\\]\n\n\\(3) Central Limit Theorems - We prove that one-dimensional random walks on discrete point processes satisfy a Central Limit Theorem. ", "We also prove that in dimension $d\\geq 2$, under the additional assumption, assumption \\[assumption3\\], the random walks on a discrete point process satisfy a Central Limit Theorem. ", "The precise statements are:\n\nLet $d=1$ and denote $e=1$ then for $P$ almost every ${{\\omega}}\\in{{\\Omega}}_0$ $$\\lim_{n\\rightarrow\\infty}{\\frac{X_n}{\\sqrt{n}}}\\overset{D}{=}N(0,{{\\mathbb{E}}}_P^2(f_{e})).$$ \\[CLT1\\]\n\nFix $d\\geq 2$. Assume the additional assumption, assumption \\[assumption3\\], then for $P$ almost every ${{\\omega}}\\in{{\\Omega}}_0$ $$\\lim_{n\\rightarrow\\infty}{\\frac{X_n}{\\sqrt{n}}}\\overset{D}{=}N(0,D),$$ where $N(0,D)$ is a d-dimensional normal distribution with covariance matrix $D$ that depends only on d and the distribution of $P$.\\[CLT2\\]\n\n**Structure of the paper.** ", "Sect. ", "2 collects some facts about the Markov chain on environments and some ergodic results related to it. ", "This section is based on previously known material. ", "In Sect. ", "3 - 4 the one dimensional case, i.e, Law of Large Numbers and Central Limit Theorem, are introduced. ", "The Recurrence Transience classification is discussed in Sec. ", "5. ", "The novel parts of the high dimensional Central Limit proof - asymptotic behavior of the random walk, construction of the corrector and sublinear bounds on the corrector - appear in Sect. ", "6-9. ", "The actual proof of the high dimensional Central Limit Theorem is carried out in Sect. ", "10. ", "Finally Sect. ", "11 contains further discussion, some open questions and conjectures.", "\n\nThe Induced shift And The Environment Seen From The Random Walk\n===============================================================\n\n$~$\\\nThe content of this section is a standard textbook material. ", "The form in which it appears here is taken from [@BB06]. ", "Even though it was all known before, [@BB06] is the best existing source for our purpose.", "\n\nLet us define the induced shift on ${{\\Omega}}_0$ as follows. ", "Let $f_e({{\\omega}})$ be as in definition \\[f\\_e\\_defn\\]. ", "By Claim \\[The\\_model\\_claim\\] we know that $f_e({{\\omega}})<\\infty$ $~Q$ almost surely Therefore we can define the maps ${{\\sigma}}_e:{{\\Omega}}_0\\rightarrow{{\\Omega}}_0$ by $${{\\sigma}}_e({{\\omega}})={{\\theta}}^{f_e({{\\omega}})}_e{{\\omega}}.$$ We call ${{\\sigma}}_e$ the induced shift.", "\n\nFor every $e\\in{{\\mathcal{E}}}$, the induced shift ${{\\sigma}}_e:{{\\Omega}}_0\\rightarrow{{\\Omega}}_0$ is $P$-preserving and ergodic with respect to $P$. \\[induced\\_shift\\_ergodicy\\]\n\nTheorem \\[induced\\_shift\\_ergodicy\\] will follow from a more general statement. ", "Let $(\\Delta,\\mathfrak{C},\\mu)$ be a probability space, and let $T:\\Delta\\rightarrow\\Delta$ be invertible, measure preserving and ergodic with respect to $\\mu$. Let $A\\in\\mathfrak{C}$ be of positive measure, and define $n:A\\rightarrow{{\\mathbb{N}}}\\cup\\{\\infty\\}$ by $$n(x)=\\min\\{k>0:T^k(x)\\in A\\}$$\\\nThe Poincaré recurrence theorem tells us that $n(x)<\\infty$ almost surely. ", "Therefore we can define, up to a set of measure zero, the map $S:A\\rightarrow A$ by $$S(x)=T^{n(x)}(x),~~~~~x\\in A$$ Then we have:\n\nS is measure preserving and ergodic with respect to $\\mu(\\cdot|A)$. It is also almost surely invertible with respect to the same measure.\\[lem\\_induced\\_shift\\_ergodicy\\]\n\n\\(1) S is measure preserving: For $j\\geq 1$, let $A_j=\\{x\\in\nA:n(x)=j\\}$. Then the $A_j~'s$ are disjoint and $\\mu\\left(A\\backslash\\cup_{j\\geq 1}{A_j}\\right)=0$. First we show that $$i\\neq j \\Rightarrow S(A_i)\\cap S(A_j)=\\emptyset.$$ To do this, we use the fact that $T$ is invertible. ", "Indeed, if $x\\in\nS(A_i)\\cap S(A_j)$ for $1\\leq i<j$, then $x=T^i(y)=T^j(z)$ for some $y,z\\in A$ with $n(y)=i,~n(z)=j$. But the fact that $T$ is invertible implies that $y=T^{j-i}(z)$, which means $n(z)\\leq\nj-i<j$, a contradiction. ", "To see that $S$ is measure preserving, we note that the restriction of $S$ to $A_j$ is $T^j$, which is measure preserving. ", "Hence, $S$ is measure preserving on $A_j$ and, since the sets $A_i$ are disjoint, $S$ is measure preserving on the union $\\cup_{j\\geq\n1}{A_j}$ as well.\\\n(2) $S$ is almost surely invertible: $S^{-1}(\\{x\\})\\cap\\{S~is~well~defined\\}$ is a one-point set by the fact that $T$ is itself invertible.\\\n(3) $S$ is ergodic: Let $B\\in\\mathfrak{C}$ be such that $B\\subset\nA$ and $0<\\mu(B)<\\mu(A)$. Assume that $B$ is $S$-invariant. ", "Then $S^n(x)\\notin A\\backslash B$ for all $x\\in B$ and all $n\\geq 1$. This means that for every $x\\in B$ and every $k\\geq 1$ such that $T^k(x)\\in A$, we have $T^k(x)\\notin A\\backslash B$. It follows that $C=\\cup_{k\\geq 1}{T^k(B)}$ is (almost surely) $T$-invariant and $\\mu(C)\\in(0,1)$, contradicting the ergodicity of $T$.\\\n\nWe know that the shift ${{\\theta}}_e$ is invertible, measure preserving and ergodic with respect to $Q$. By Lemma (\\[lem\\_induced\\_shift\\_ergodicy\\]) the induced shift is $P$-preserving, almost surely invertible and ergodic with respect to $P$.\\\n\nUnder the present circumstances, Theorem \\[induced\\_shift\\_ergodicy\\] has one important corollary:\n\nLet $B\\in\\mathcal{B}$ be a subset of ${{\\Omega}}_0$ such that for almost every ${{\\omega}}\\in B$ $$P_{{\\omega}}({{\\theta}}_{X_1}{{\\omega}}\\in B)=1. ", "\\label{The_Lemma_0-1_Law}$$ Then $B$ is a zero-one event under $P$. \\[lemma\\_sec2\\]\n\nThe Markov property and (\\[The\\_Lemma\\_0-1\\_Law\\]) imply that $P_{{\\omega}}({{\\theta}}_{X_n}{{\\omega}}\\in B)=1$ for all $n\\geq 1$ and that $P$-almost every ${{\\omega}}\\in B$. We claim that ${{\\sigma}}_e({{\\omega}})\\in B$ for $P$-almost surely ${{\\omega}}\\in B$. Indeed, let ${{\\omega}}\\in B$ be such that ${{\\theta}}_{X_n}{{\\omega}}\\in B$ for all $n\\geq 1$, $P_{{\\omega}}$-almost surely. ", "note that we have $f_e({{\\omega}})e\\in{{\\mathcal{P}}}({{\\omega}})$. Therefore we have $P_{{\\omega}}(X_1=f_e({{\\omega}})e)=\\frac{1}{2d}>0$. This means that ${{\\sigma}}_e({{\\omega}})={{\\theta}}^{n({{\\omega}})}_e({{\\omega}})\\in B$, i.e., $B$ is almost surely ${{\\sigma}}_e$-invariant. ", "By the ergodicy of the induced shift, $B$ is a zero-one event.", "\n\nOur next goal will be to prove that the Markov chain on environments is ergodic. ", "Let $\\Xi={{\\Omega}}_0^{{{\\mathbb{Z}}}}$ and define $\\mathscr{H}$ to be the product ${{\\sigma}}$-algebra on $\\Xi$. The space $\\Xi$ is a space of two-sided sequences - $(\\ldots,{{\\omega}}_{-1},{{\\omega}}_0,{{\\omega}}_1,\\ldots)$ - the trajectories of the Markov chain on environments. ", "Let $\\mu$ be the measure on $(\\Xi,\\mathscr{H})$ such that for any $B\\in\\mathcal{B}^{2n+1}$, $$\\mu\\big(({{\\omega}}_{-n},\\ldots,{{\\omega}}_n)\\in B\\big)=\\int_{B}{P(d{{\\omega}}_{-n})\\Lambda({{\\omega}}_{-n},d{{\\omega}}_{-n+1})\\ldots\\Lambda({{\\omega}}_{n-1},d{{\\omega}}_n)},$$ where $\\Lambda:{{\\Omega}}_0\\times\\mathcal{B}\\rightarrow [0,1]$ is the Markov kernel defined by $$\\Lambda({{\\omega}},A)=\\frac{1}{2d}\\sum_{x\\in{{\\mathbb{Z}}}^d}{\\big(\\mathbbm{1}_{\\{x\\in\nN_0({{\\omega}})\\}}\\mathbbm{1}_{\\{{{\\theta}}^x{{\\omega}}\\in A\\}}\\big)}. ", "\\label{Lambda}$$ Note that the sum is finite since for almost every ${{\\omega}}\\in{{\\Omega}}$ there are exactly $2d$ elements in $N_0({{\\omega}})$. $\\mu$ exists and is unique by Kolmogorov’s Theorem, because $P$ is preserved by $\\Lambda$, and therefore the finite dimensional measures are consistent. ", "$\\{{{\\theta}}_{X_k}({{\\omega}})\\}_{k\\geq 0}$ has the same law in ${{\\mathbb{E}}}_P(P_{{\\omega}}(\\cdot))$ as $({{\\omega}}_0,{{\\omega}}_1,\\ldots)$ has in $\\mu$. Let $\\widetilde{T}:\\Xi\\rightarrow\\Xi$ be the shift defined by $(\\widetilde{T}{{\\omega}})_n={{\\omega}}_{n+1}$. Then $\\widetilde{T}$ is measure preserving.", "\n\n$\\widetilde{T}$ is ergodic with respect to $\\mu$. \\[ergodic\\_particle\\_view\\]\n\nLet $E_\\mu$ denote expectation with respect to $\\mu$. Pick $A\\subset\\Xi$ that is measurable and $\\widetilde{T}$-invariant. ", "We need to show that $\\mu(A)\\in\\{0,1\\}$.\\\nLet $f:{{\\Omega}}_0\\rightarrow{{\\mathbb{R}}}$ be defined as $f({{\\omega}}_0)=E_\\mu(\\mathbbm{1}_A|{{\\omega}}_0).$ First we claim that $f=\\mathbbm{1}_A$ almost surely. ", "Indeed, since $A$ is $\\widetilde{T}$-invariant, there exist $A_+\\in{{\\sigma}}({{\\omega}}_k:k>0)$ and $A_-\\in{{\\sigma}}({{\\omega}}_k:k<0)$ such that $A$ and $A_\\pm$ differ only by null sets from one another (This follows by approximation of $A$ by finite-dimensional events and using the $\\widetilde{T}$-invariance of $A$). ", "Now, conditional on ${{\\omega}}_0$, the event $A_+$ is independent of ${{\\sigma}}({{\\omega}}_k:k<0)$ and so L$\\acute{e}$vy’s Martingale Convergence Theorem gives us $$E_\\mu(\\mathbbm{1}_A|{{\\omega}}_0)=E_\\mu(\\mathbbm{1}_{A_+}|{{\\omega}}_0,{{\\omega}}_{-1},\\ldots,{{\\omega}}_{-n})$$ $$=E_\\mu(\\mathbbm{1}_{A_-}|{{\\omega}}_0,\\ldots,{{\\omega}}_{-n})~\\overrightarrow{_{n\\rightarrow\\infty}}~\\mathbbm{1}_{A_-}=\\mathbbm{1}_A,$$ with equalities valid $\\mu$-almost surely. ", "Next let $B\\subset{{\\Omega}}_0$ be defined by $B=\\{{{\\omega}}_0:f({{\\omega}}_0)=1\\}$. Clearly $B$ is $\\mathfrak{B}$-measurable and, since the ${{\\omega}}_0$-marginal of $\\mu$ is $P$, $$\\mu(A)=E_\\mu(f)=P(B)$$ Hence, in order to prove that $\\mu(A)\\in\\{0,1\\}$, we need to show that $P(B)\\in\\{0,1\\}$ But $A$ is $\\widetilde{T}$-invariant and so, up to set of measure zero, if ${{\\omega}}_0\\in B$ then ${{\\omega}}_1\\in B$. This means that $B$ satisfies the condition of the lemma \\[lemma\\_sec2\\], and so $B$ is a zero-one event.\\\n\nLet $f\\in L^1({{\\Omega}}_0,\\mathcal{B},P)$. Then for $P$-almost all ${{\\omega}}\\in{{\\Omega}}_0$ $$\\lim_{n\\rightarrow\\infty}{\\frac{1}{n}\\sum_{k=0}^{n-1}{f\\circ{{\\theta}}_{X_k}({{\\omega}})}={{\\mathbb{E}}}_P(f)}~~~~~~P_{{\\omega}}~almost~surely.$$ Similarly, if $f:{{\\Omega}}\\times{{\\Omega}}\\rightarrow{{\\mathbb{R}}}$ is measurable with ${{\\mathbb{E}}}_P(E_{{\\omega}}(f({{\\omega}},{{\\theta}}_{X_1}{{\\omega}})))<\\infty$, then $$\\lim_{n\\rightarrow\\infty}{\\frac{1}{n}\\sum_{k=0}^{n-1}{f({{\\theta}}_{X_k}{{\\omega}},{{\\theta}}_{X_{k+1}}{{\\omega}})}={{\\mathbb{E}}}_P(E_{{\\omega}}(f({{\\omega}},{{\\theta}}_{X_1}{{\\omega}})))}.$$ for $P$-almost all ${{\\omega}}$ and $P_{{\\omega}}$-almost all trajectories of $(X_k)_{k\\geq 0}$. \\[Thm\\_mutual\\_ergodic\\]\n\nRecall that $\\{{{\\theta}}_{X_k}({{\\omega}})\\}_{k\\geq 0}$ has the same law in ${{\\mathbb{E}}}_P(P_{{\\omega}}(\\cdot))$ as $({{\\omega}}_0,{{\\omega}}_1,\\ldots)$ has in $\\mu$. Hence, if $g(\\ldots,{{\\omega}}_{-1},{{\\omega}}_0,{{\\omega}}_1,\\ldots)=f({{\\omega}}_0)$ then $$\\lim_{n\\rightarrow\\infty}{\\frac {1}{n}\\sum_{k=0}^{n-1}{f\\circ{{\\theta}}_{X_k}}}\\overset{D}{=}\\lim_{n\\rightarrow\\infty}{\\frac{1}{n}\\sum_{k=0}^{n-1}{g\\circ\n\\widetilde{T}^k}}.$$ The latter limit exists by Birkhoff’s Ergodic Theorem (we have already seen that $\\widetilde{T}$ is ergodic) and equals $E_\\mu(g)={{\\mathbb{E}}}_P(f)$ almost surely. ", "The second part is proved analogously.", "\n\nLaw of Large Numbers\n====================\n\nWe turn now to prove Theorem \\[LLN\\] - i.e. Law of Large Numbers for random walks on a discrete point process. ", "For completeness we state the theorem again:\n\n***\\[LLN\\]*** Define the event $$A=\\left\\{\\lim_{n\\rightarrow\\infty}{\\frac{X_n}{n}}=0\\right\\}.$$ Then ${{\\mathbb{P}}}(A)=1.$\n\nUsing linearity, it is enough to prove that for every $e\\in{{\\mathcal{E}}}$ we have ${{\\mathbb{P}}}(A_e)=1$, where $$A_e=\\left\\{\\lim_{n\\rightarrow\\infty}{\\frac{X_n\\cdot e}{n}}=0\\right\\}.$$ For every $e\\in{{\\mathcal{E}}}$ let $f_e$ be as in Definition \\[f\\_e\\_defn\\]. ", "By (\\[The\\_model\\_claim\\]) $f_e$ is $P$-a.s finite. ", "We first prove that ${{\\mathbb{E}}}_P(f_e)<\\infty$. Assume for contradiction that ${{\\mathbb{E}}}_P(f_e)=\\infty$, since $f_e$ is positive then $$\\lim_{n\\rightarrow\\infty}{\\frac{1}{n}\\sum_{k=0}^{n-1}{f_e({{\\sigma}}_e^k({{\\omega}}))}}=\\infty~~~~~P~a.s.", "\n\\label{lim_f}$$ Indeed, for every $M>0$ define $$f_e^M({{\\omega}})=\n\\left\\{\n\\begin{array}{cc}\n f_e({{\\omega}}) & f_e({{\\omega}})\\leq M \\\\\n M & f_e({{\\omega}})>M \\\\\n\\end{array}\n\\right.", ",$$ then, since $f_e^M$ is finite by Birkhoff Ergodic Theorem $$\\lim_{n\\rightarrow\\infty}{\\frac{1}{n}\\sum_{k=0}^{n-1}{f_e({{\\sigma}}_e^k({{\\omega}}))}}\\geq\\lim_{n\\rightarrow\\infty}{\\frac{1}{n}\\sum_{k=0}^{n-1}{f_e^M({{\\sigma}}_e^k({{\\omega}}))}}={{\\mathbb{E}}}_P(f_e^M),~~~~~P~a.s.$$ Taking now M to infinity we get $$\\lim_{n\\rightarrow\\infty}{\\frac{1}{n}\\sum_{k=0}^{n-1}{f_e({{\\sigma}}_e^k({{\\omega}}))}}\\geq\\lim_{M\\rightarrow\\infty}{{{\\mathbb{E}}}_P(f_e^M)}={{\\mathbb{E}}}_P(f_e)=\\infty,~~~~~P~a.s.$$ Let $S(k)=max\\left\\{n\\geq\n0:\\sum_{m=0}^{n-1}{f({{\\sigma}}_e^m({{\\omega}}))}<k\\right\\}$, by (\\[lim\\_f\\]) $$\\lim_{k\\rightarrow\\infty}{\\frac{S(k)}{k}}=0~~~~~P~a.s.$$\\\nOn the other hand, let $g:{{\\Omega}}\\rightarrow\\{0,1\\}$ be defined by $$g({{\\omega}})=\\mathbbm{1}_{{{\\Omega}}_0}({{\\omega}}),$$ then $$S(k)=\\sum_{j=0}^{k-1}{g({{\\theta}}_e^j({{\\omega}}))},$$ and therefore by Birkhoff’s Ergodic Theorem $$Q({{\\Omega}}_0)=\\lim_{k\\rightarrow\\infty}{\\frac{1}{k}\\sum_{j=0}^{k-1}{g({{\\theta}}_e^j({{\\omega}}))}}=\\lim_{k\\rightarrow\\infty}{\\frac{S(k)}{k}}=0,~~~~~P~a.s,$$ contradicting assumption \\[Assumptions\\]. ", "It follow that ${{\\mathbb{E}}}_P(f_e)<\\infty$, and therefore by Birkhoff Ergodic Theorem $$\\lim_{n\\rightarrow\\infty}{\\frac{1}{n}\\sum_{k=0}^{n-1}{f_e({{\\sigma}}_e^k({{\\omega}}))}}={{\\mathbb{E}}}_P(f_e)<\\infty~~~~~P~a.s.\\label{Finite_sum_of_changes}$$\n\nNotice that $$P(f_{-e}({{\\omega}})=k)=P(f_e({{\\sigma}}_e^{-1}({{\\omega}}))=k)=P(f_e({{\\omega}})=k),\\label{Symmetry}$$ where the last equality is true since $P$ is stationary. ", "It therefore follows that $${{\\mathbb{E}}}_P(f_e)={{\\mathbb{E}}}_P(f_{-e}) \\label{Expectation_equality}$$\n\nFor $e\\in{{\\mathcal{E}}}$ let $g_e:{{\\Omega}}\\times{{\\Omega}}\\rightarrow{{\\mathbb{Z}}}$ be as follows: $$g_e({{\\omega}},{{\\omega}}')= \\left\\{\n\\begin{array}{cc}\nf_e({{\\omega}}) & {{\\omega}}'={{\\sigma}}_e({{\\omega}}) \\\\\n-f_{-e}({{\\omega}}) & {{\\omega}}'={{\\sigma}}_{-e}({{\\omega}}) \\\\\n0 & otherwise \\end{array}\\right..$$ Now, $g_e$ is measurable and using (\\[Expectation\\_equality\\]) we get $${{\\mathbb{E}}}_P(E_{{\\omega}}(g_e({{\\omega}},{{\\theta}}^{X_1}{{\\omega}})))={{\\mathbb{E}}}_P\\left(\\frac{1}{2d}f_e({{\\omega}})-\\frac{1}{2d}f_{-e}({{\\omega}})\\right)=0.$$ It therefore follows that for every $e\\in{{\\mathcal{E}}}$, for almost every ${{\\omega}}\\in{{\\Omega}}_0$ and $P_{{\\omega}}$ almost every random walk $\\{X_k\\}_{k\\geq\n0}$, we have for $Z_k=X_k-X_{k-1},~~k\\geq 1$ that $$\\lim_{n\\rightarrow\\infty}{\\frac{X_n\\cdot e}{n}}=\\lim_{n\\rightarrow\\infty}{\\frac{1}{n}\\sum_{k=1}^{n}{Z_k\\cdot e}},$$ and from this equals to $$\\lim_{n\\rightarrow\\infty}{\\frac{1}{n}\\sum_{k=0}^{n-1}{g_e({{\\theta}}_{X_k}{{\\omega}},{{\\theta}}_{X_{k+1}}{{\\omega}})}}={{\\mathbb{E}}}_P(E_{{\\omega}}(g_e({{\\omega}},{{\\theta}}_{X_1}{{\\omega}})))=0,~~~{{\\mathbb{P}}}~a.s.$$\n\nOne Dimensional Central Limit Theorem\n=====================================\n\nHere we prove Theorem \\[CLT1\\] - i.e. Central Limit Theorem for one dimensional random walks on discrete point processes. ", "We start by stating the theorem\n\n***\\[CLT1\\]*** Let $d=1$ and denote $e=1$ then for $P$ almost every ${{\\omega}}\\in{{\\Omega}}_0$ $$\\lim_{n\\rightarrow\\infty}{\\frac{X_n}{\\sqrt{n}}}\\overset{D}{=}N(0,{{\\mathbb{E}}}_P^2(f_{e})).$$\n\nWe first notice that for $d=1$, a random walk on a discrete point process is almost surely a simple one dimensional random walk with changed distances between points. ", "Secondly the expectation of the distance between points, given by ${{\\mathbb{E}}}_P(f_{e})$, is finite.", "\n\nGiven an environment ${{\\omega}}\\in{{\\Omega}}_0$ and a random walk $\\{X_k\\}_{k\\geq\n0}$, we define the simple one-dimensional random walk $\\{Y_k\\}_{k\\geq 0}$ associated with $\\{X_k\\}_{k\\geq 0}$ as follows: First we define $Z_k=X_k-X_{k-1}$ for every $k\\geq 1$, then we define $W_k=\\frac{Z_k}{|Z_k|}$. Finally we define $Y_0=0$ and for $k\\geq 1$ we define $Y_k=\\sum_{j=1}^{k}{W_k}$. Since $\\{Y_k\\}_{k\\geq\n0}$ is a simple one dimensional random walk on ${{\\mathbb{Z}}}$, it follows from the Central Limit Theorem that for $P$ almost every ${{\\omega}}\\in{{\\Omega}}_0$ $$\\lim_{n\\rightarrow\\infty}{\\frac{1}{\\sqrt{n}}\\cdot\nY_n}\\overset{D}{=}N(0,1).$$\n\nWe now turn to define for every ${{\\omega}}\\in{{\\Omega}}$ the points of the environment. ", "For every $n\\in{{\\mathbb{Z}}}$ let $t_n$ be the $n^{\\mbox{th}}$ place on the grid with a point, i.e. $t_0=0$, $$t_n=\\sum_{k=0}^{n-1}{f_{e}({{\\sigma}}_e^k{{\\omega}})}~~~~~n>0,$$ and $$t_n=\\sum_{k=-1}^{-n}{f_{e}({{\\sigma}}_e^k{{\\omega}})}~~~~~n<0.$$\n\nFor every $a>0$ we have $$\\lim_{n\\rightarrow\\infty}{\\frac{1}{\\sqrt{n}}t_{\\lfloor a\\sqrt{n}\\rfloor}}\n=a\\cdot\\lim_{n\\rightarrow\\infty}{\\frac{1}{a\\sqrt{n}}\\sum_{k=0}^{\\lfloor\na\\sqrt{n}\\rfloor}{f_{e}({{\\sigma}}_e^k{{\\omega}})}}=a\\cdot {{\\mathbb{E}}}_P(f_{e}),$$ where the last equality holds since this sequence contain the same elements as the sequence in (\\[Finite\\_sum\\_of\\_changes\\]) and every element in the original sequence appears only a finite number of times, therefore those sequences have the same partial limits, and the original sequence (the one in ) converges.", "\n\nBy the same argument for every $a\\in{{\\mathbb{R}}}$ we have that $$\\lim_{n\\rightarrow\\infty}{\\frac{1}{\\sqrt{n}}t_{\\lfloor\na\\sqrt{n}\\rfloor}}=a\\cdot {{\\mathbb{E}}}_P(f_{e}). ", "\\label{limit_CLT_constant}$$\n\nUsing (\\[limit\\_CLT\\_constant\\]) and the fact that $\\lim_{n\\rightarrow\\infty}{\\frac{Y_n}{\\sqrt{n}}}$ exists and finite ${{\\mathbb{P}}}$ almost surely, we get that $$\\lim_{n\\rightarrow\\infty}{\\frac{1}{\\sqrt{n}}t_{Y_n}}=\\lim_{n\\rightarrow\\infty}{\\frac{1}{\\sqrt{n}}t_{\\frac{Y_n}{\\sqrt{n}}\\sqrt{n}}}\\leq\na~~\\Leftrightarrow~~\\lim_{n\\rightarrow\\infty}{\\frac{Y_n}{\\sqrt{n}}\\leq\\frac{a}{{{\\mathbb{E}}}_P(f_{e})}},$$ and therefore $${{\\mathbb{P}}}\\left(\\lim_{n\\rightarrow\\infty}{\\frac{1}{\\sqrt{n}}t_{Y_n}}\\leq a\\right)\n={{\\mathbb{P}}}\\left(\\lim_{n\\rightarrow\\infty}{\\frac{Y_n}{\\sqrt{n}}\\leq\\frac{a}{{{\\mathbb{E}}}_P(f_{e})}}\\right)=\\Phi\\left(\\frac{a}{{{\\mathbb{E}}}_P(f_{e})}\\right),$$ where $\\Phi$ is the standard normal cumulative distribution function. ", "Finally, we notice that $$X_n=t_{Y_n},$$ and therefore we conclude that $${{\\mathbb{P}}}\\left(\\lim_{n\\rightarrow\\infty}{\\frac{X_n}{\\sqrt{n}}}\\leq\na\\right)=\\Phi\\left(\\frac{a}{{{\\mathbb{E}}}_P(f_{e})}\\right),$$ as required.", "\n\nTransience and Recurrence\n=========================\n\nBefore we continue the discussion on Central Limit Theorem in higher dimensions, we turn to deal with transience and recurrence of random walks on discrete point processes.", "\n\nOne-dimensional case\n--------------------\n\n***\\[tran\\_recu1\\]*** The one dimensional random walk on a discrete point process is ${{\\mathbb{P}}}$-almost surely recurrent.", "\n\nUsing the notation from the previous section, since $Y_n$ is a one-dimensional simple random walk, it is recurrent ${{\\mathbb{P}}}$ almost surely. ", "Therefore we have $\\#\\{n:Y_n=0\\}=\\infty~~{{\\mathbb{P}}}$ almost surely, but since $X_n=t_{Y_n}$ and $t_0=0$ we have $\\#\\{n:X_n=0\\}=\\infty~~{{\\mathbb{P}}}$ almost surely, and therefore the random walk is recurrent.", "\n\nTwo-dimensional case\n--------------------\n\nThe theorem we wish to prove is the following:\n\n***\\[tran\\_recu2\\]*** Let $({{\\Omega}},{{\\mathfrak{B}}},P)$ be a two dimensional discrete point process and assume there exists a constant $C>0$ such that $$\\sum_{k=N}^{\\infty}{\\frac{k\\cdot\nP(f_{e_i}=k)}{{{\\mathbb{E}}}(f_{e_i})}}\\leq\\frac{C}{N},\\quad\\forall\ni\\in\\{1,2\\}~~\\forall N\\in{{\\mathbb{N}}}, \\label{Cauchy_tail_ass}$$ which in particular holds, whenever $f_{e_i}$ has a second moment for $i\\in\\{1,2\\}$. Then the random walk is ${{\\mathbb{P}}}$ almost surely recurrent.", "\n\nThe proof is based on the connection between random walks, electrical networks and the Nash-William criteria for recurrence of random walks. ", "For a proof of the Nash-William criteria and some background on the subject see [@DS84] and [@LP97].", "\n\nWe start with the following definition:\n\nLet $(\\widetilde{{{\\Omega}}},\\widetilde{\\mathfrak{B}},\\widetilde{P})$ be a probability space. ", "We say that a random variable $X:\\widetilde{{{\\Omega}}}\\rightarrow [0,\\infty)$ has a Cauchy tail if there exist a positive constant $C$ such that for every $n\\in {{\\mathbb{N}}}$ we have $$\\widetilde{P}\\left(X\\geq n\\right)\\leq \\frac{C}{n}. ", "\\nonumber$$ Note that if $\\widetilde{E}(X)<\\infty$, then X has a Cauchy tail.", "\n\nIn order to prove theorem \\[tran\\_recu2\\] we will need the following lemmas taken from [@Be01].", "\n\nLet $\\{f_i\\}_{i=1}^{\\infty}$ be identically distributed positive random variables, on a probability space $(\\widetilde{{{\\Omega}}},\\widetilde{\\mathfrak{B}},\\widetilde{P})$, that have a Cauchy tail. ", "Then, for every $\\epsilon>0$, there exist $K>0$ and $N\\in{{\\mathbb{N}}}$\n\nsuch that for every $n>N$ $$\\widetilde{P}\\left(\\frac{1}{n}\\sum_{k=0}^{n}{f_i}>K\\log n\\right)<\\epsilon.$$ \\[Cauchy\\_tail\\_lemma\\]\n\n$f_i$ has a Cauchy tail, so there exists $C_0$ such that for every $n\\in{{\\mathbb{N}}}$ $$\\widetilde{P}(f_i>n)<\\frac{C_0}{n}$$ Let $M>\\frac{2}{{{\\epsilon}}}$ be a large number, and $N$ large enough that $C_0N^{1-M}<\\frac{{{\\epsilon}}}{2}$. Fix $n>N$, and let $g_i=\\min\\{f_i,n^M\\}$ for all $1\\leq i\\leq n$. Then, $$\\widetilde{P}\\left(\\frac{1}{n}\\sum_{i=1}^{n}{f_i}\\neq\\frac{1}{n}\\sum_{i=1}^{n}{g_i}\\right)\\leq\\sum_{k=1}^{n}{\\widetilde{P}(f_k\\neq g_k)}=n\\cdot \\widetilde{P}(f_1\\neq g_1).$$ The last term is equal to $$n\\cdot \\widetilde{P}(f_1>n^M)<\\frac{n\\cdot C_0}{n^M}<\\frac{{{\\epsilon}}}{2}.$$ Now, since $E(g_i)\\leq C_0M \\log n$, and $g_i$ is positive, by Markov’s inequality, choosing $K=C_0M^2$ we get $$\\widetilde{P}\\left(\\frac{1}{n}\\sum_{i=1}^{n}{g_i}>K\\log n\\right)<\\frac{C_0M\\log n}{C_0M^2\\log n}=\\frac{1}{M}<\\frac{{{\\epsilon}}}{2}$$ and so $$\\widetilde{P}\\left(\\frac{1}{n}\\sum_{i=1}^{n}{f_i}>K\\log n\\right)<{{\\epsilon}}$$\\\n\nLet $A_n$ be a sequence of events such that $\\tilde{P}(A_n)>1-\\epsilon$ for all sufficiently large $n$, and let $\\{a_n\\}_{n=1}^\\infty$ be a sequence such that $$\\sum_{n=1}^{\\infty}{a_n}=\\infty.$$ Then, with probability of at least $1-{{\\epsilon}}$ $$\\sum_{n=1}^{\\infty}{\\mathbbm{1}_{A_n}\\cdot a_n}=\\infty.$$ \\[lem2\\_2dim\\_recurrent\\]\n\nIt is enough to show that there exists $N$ such that for any $M$, $$P\\left(\\sum_{n=N}^{\\infty}{\\mathbbm{1}_{A_n}\\cdot\na_n}<M\\right)\\leq{{\\epsilon}}. ", "\\label{lem_claim}$$ Define $N$ such that for every $n>N$ we have $P(A_n)>1-\\epsilon$, and assume that for some $M$ (\\[lem\\_claim\\]) is false. ", "Define $B_M$ to be the event $$B_M=\\left\\{\\sum_{n=N}^{\\infty}{\\mathbbm{1}_{A_n}\\cdot a_n}<M\\right\\}.$$ Since $P(B_M)>{{\\epsilon}}$, we know that there exist $\\delta>0$ such that for every $n$ $$P(A_n|B_M)=\\frac{P(A_n\\cap B_M)}{P(B_M)}\\geq\\frac{P(B_M)-{{\\epsilon}}}{P(B_M)}>\\delta>0.$$ Therefore, $$E\\left[\\sum_{n=N}^{\\infty}{\\mathbbm{1}_{A_n}\\cdot a_n}\\Bigg|B_M\\right]\\geq\\delta\\sum_{n=N}^{\\infty}{a_n}=\\infty,$$ which contradicts the definition of $B_M$.\\\n\nIn the proof of Theorem \\[tran\\_recu2\\] we will use the following notation: Given a graph $G=(V,E)$ with $V\\subset{{\\mathbb{Z}}}^d$, for every $e\\in E$ define $e^+\\in V$ and $e^-\\in V$ to be the end points of $e$, such that if $(e^+-e^-)\\cdot e_i\\neq 0$ then $(e^+-e^-)\\cdot\ne_i>0$. In addition for every $e\\in E$ we write $l(e)=|e^+-e^-|_1$.\n\nFor every ${{\\omega}}\\in{{\\Omega}}$, we define the corresponding network with conductances $G({{\\omega}})=(V({{\\omega}}),E({{\\omega}}),c({{\\omega}}))$ as follows: First let $G''({{\\omega}})=(V''({{\\omega}}),E''({{\\omega}}),c''({{\\omega}}))$ be the network with $V''({{\\omega}})={{\\mathcal{P}}}({{\\omega}})$ and $E''({{\\omega}})=\\{\\{x,y\\}\\in V''\\times\nV'':y\\in\\{x\\pm f_{e_1}({{\\omega}})e_1,x\\pm f_{e_2}({{\\omega}})e_2\\}\\}$, i.e. the set of edges from each point to its four “nearest neighbors”. ", "we also define the conductance $c''({{\\omega}})(e)=1$ for every $e\\in\nE''({{\\omega}})$. We now define $G'({{\\omega}})$ to be the network generated from $G''({{\\omega}})$ by “cutting” every edge of length $k$ into $k$ edges of length $1$, each cut with conductance $k$. Formally we define $V'({{\\omega}})=V^1({{\\omega}})\\biguplus\nV^2({{\\omega}})\\subset{{\\mathbb{Z}}}^2\\times\\{0,1\\}$ where\n\n$$V^i({{\\omega}})=\\left\\{(x,i):\\begin{array}{cc} \\exists~e\\in E''({{\\omega}})\n~\\exists~0\\leq k\\leq l(e)\\\\~such~that~(e^+-e^-)\\cdot e_i\\neq\n0~\\wedge~x=e^-+ke_i\\end{array}\\right\\},$$\n\nand we define $E'({{\\omega}})=E^1({{\\omega}})\\cup E^2({{\\omega}})$ by\n\n$$E^i({{\\omega}})=\\left\\{\\left\\{(v,i),(w,i)\\right\\}:\\begin{array}{cc} \\exists~e\\in E''({{\\omega}})~\\exists~0\\leq k<\nl(e)~~such~that~\\\\~(e^+-e^-)\\cdot e_i\\neq 0~\\wedge\nv=e^-+ke_i,w=e^-+(k+1)e_i\\end{array}\\right\\}.$$ We also define the conductance $c'({{\\omega}})(e)$ of an edge $e\\in E'({{\\omega}})$ to be $k$, given that the length of the original edge it was part of was $k$. Finally we define $G({{\\omega}})$ to be the graph generated from $G'({{\\omega}})$ by identifying every $v\\in V''({{\\omega}})$ on both levels i.e, we take the graph $G'({{\\omega}})$ modulo the equivalence relations $(v,1)=(v,2)~~\\forall~v\\in V''({{\\omega}})$. We now turn to prove the recurrence using the Nash-Williams Criteria. ", "Let $\\Pi_n$ be the set of edges exiting the box $([-n,n]\\times [-n,n],[1,2])$ in the graph $G({{\\omega}})$. Then $\\Pi_n$ defines a sequence of pairwise disjoint cutsets in the network $G({{\\omega}})$. Let $e\\in\\Pi_n$ be such that $(e^+-e^-)\\cdot e_i\\neq 0$ then $${{\\mathbb{P}}}(c(e)=k)={{\\mathbb{P}}}\\left(\\begin{array}{cc}\\text{the original edge that contained}\\\\\ne \\text{ is of length } k\\end{array}\\right)=\\frac{k\\cdot\n{{\\mathbb{P}}}(f_{e_i}=k)}{{{\\mathbb{E}}}(f_{e_i})}.$$ Indeed, the probability that the edge e was part of an edge of length $k$ in the original graph, needs to be multiplied by $k$, since it can be in any part of the edge. ", "From assumption it follows that $c(e)$ has a Cauchy tail. ", "In $\\Pi_n$ there are $2n+4$ edges in the first level and $2n+4$ in the second level, all of them with the same distribution (and by a Cauchy tail), though they may be dependent. ", "By Lemma \\[Cauchy\\_tail\\_lemma\\], for every ${{\\epsilon}}>0$ there exist $K>0$ and $N\\in{{\\mathbb{N}}}$ such that for every $n>N$, we have $${{\\mathbb{P}}}\\left(\\sum_{e\\in\\Pi_n}{C(e)}\\leq K(4n+8)\\log 4n+8\\right)>1-{{\\epsilon}}.", "\n\\label{Cauchy_event}$$\n\nDefine $A_n$ to be the event in equation (\\[Cauchy\\_event\\]), and set $a_n=(K(4n+8)\\log (4n+8))^{-1}$ for $n\\geq N$. Now, $$\\sum_{n=1}^{\\infty}{{C_{\\Pi_n}}^{-1}}\\geq\n\\sum_{n=N}^{\\infty}{\\mathbbm{1}_{A_n}\\cdot a_n}.$$ By the definition of $\\{a_n\\}$, $$\\sum_{n=N}^{\\infty}{a_n}=\\infty.$$ On the other hand, ${{\\mathbb{P}}}(A_n)>1-{{\\epsilon}}$ for all n. So by Lemma \\[lem2\\_2dim\\_recurrent\\], $${{\\mathbb{P}}}\\left(\\sum_{n=1}^{\\infty}{{C_{\\Pi_n}}^{-1}}=\\infty\\right)\\geq 1-{{\\epsilon}}.$$ Since ${{\\epsilon}}$ is arbitrary, we get that ${{\\mathbb{P}}}$ a.s. ", "$$\\sum_{n=1}^{\\infty}{{C_{\\Pi_n}}^{-1}}=\\infty.$$ Therefore by the Nash-Williams criteria, the random walk is ${{\\mathbb{P}}}$ almost surely recurrent on $G({{\\omega}})$.\n\nHigher dimensions ($d\\geq 3$)\n-----------------------------\n\n$~$\\\nWe start by stating the theorem:\n\n***\\[tran\\_recu3\\]*** Let $({{\\Omega}},{{\\mathfrak{B}}},P)$ be a $d$-dimensional discrete point process $d\\geq\n3$ then the random walk is ${{\\mathbb{P}}}$ almost surely transient.\\\n\nThe main idea beyond the proof is as follows: first we show that the boundary of every set of volume $n$ in ${{\\mathbb{Z}}}^d$ is at least a positive constant times $n^{\\frac{d-1}{d}}$, then we will use the known fact that for every graph $G=(V,E)$ with bounded degree, such that for every set of vertices of volume $n$, the boundary is at least a constant times $n^\\alpha$, with $\\alpha>\\frac{1}{2}$, a simple random walk on G is transient.", "\n\nWe start by proving an isoperimetric inequality.", "\n\nLet $A=\\{x^i=(x_1^i,x_2^i,\\ldots,x_d^i)\\}_{i=1}^n$ be a finite subset of ${{\\mathbb{Z}}}^d$. We define $\\Pi^j:{{\\mathbb{Z}}}^d\\rightarrow{{\\mathbb{Z}}}^{d-1}$ to be the projection on all but the $j^{th}$ coordinate, i.e, $\\Pi^j(x)=\\Pi^j((x_1,x_2,\\ldots,x_d))=(x_1,x_2,\\ldots,x_{j-1},x_{j+1},\\ldots,x_d)$. Define $A_j=\\Pi^j(A)$. Then there exists $C>0$ such that $$\\max_{1\\leq j\\leq d}\\{|A_j|\\}\\geq C\\cdot |A|^{\\frac{d-1}{d}},$$ where $|\\cdot|$ denotes the cardinality of the set. ", "\\[lem\\_volume\\_surface\\]\n\nUsing translation, we can assume without loss of generality that $x_j^i>0$ for every $1\\leq i\\leq n$ and $1\\leq j \\leq d$. For every point $x$ in the quadrat, where all coordinates are positive, we define the energy of a point $\\mathcal{E}(x)$ by $$\\mathcal{E}(x)=x\\cdot (1,1,\\ldots,1)=\\sum_{j=1}^d x_j.$$ In addition we define the energy of a finite set A in this quadrat as $$\\mathcal{E}(A)=\\sum_{x\\in A}{\\mathcal{E}(x)}.$$ For each point $(x_2,x_3,\\ldots,x_d)$ in ${{\\mathbb{Z}}}^{d-1}$ with positive entries we define the set $A_{(x_2,x_3,\\ldots,x_d)}=\\{x_1:(x_1,x_2,\\ldots,x_d)\\in A\\}$, which we will call the $(x_2,x_3,\\ldots,x_d)$ fiber of $A$. ", "We now define a new set $A^1$, with the following property: For each point $(x_2,x_3,\\ldots,x_d)$ in ${{\\mathbb{Z}}}^{d-1}$ the $(x_2,x_3,\\ldots,x_d)$ fiber of $A$ as the same size as the $(x_2,x_3,\\ldots,x_d)$ fiber of $A^1$, and in addition the $(x_2,x_3,\\ldots,x_d)$ fiber of $A^1$ is the one with least energy (when thought as a set in ${{\\mathbb{Z}}}$). ", "We claim that the following set fulfills this property: $$A^1=\\bigcup_{x_2\\in{{\\mathbb{N}}}}\\bigcup_{x_3\\in{{\\mathbb{N}}}}\\ldots\\bigcup_{x_d\\in{{\\mathbb{N}}}}{\\{(a,x_2,x_3,\\ldots,x_d):a\\in{{\\mathbb{N}}}~\\wedge~1\\leq\na\\leq |A_{(x_2,x_3,\\ldots,x_d)}|\\}}.$$\n\nIndeed, the $(x_2,x_3,\\ldots,x_d)$ fiber of $A^1$ is $\\{(a,x_2,x_3,\\ldots,x_d):a\\in{{\\mathbb{N}}}~\\wedge~1\\leq a\\leq\n|A_{(x_2,x_3,\\ldots,x_d)}|\\}$ which has the same size as the $(x_2,x_3,\\ldots,x_d)$ fiber of $A$. ", "In addition, for any fixed $m\\in{{\\mathbb{N}}}$, the unique set $B\\subset{{\\mathbb{N}}}$ of size $m$ and minimal energy is $B=\\{1,2,\\ldots,m\\}$.\n\nTherefore the set $A^1$ has the following properties:\n\n1. ", " $|A^1|=n$.\\\n\n2. ", " $|\\Pi^j(A^1)|\\leq |\\Pi^j(A)|$ for every $1\\leq j \\leq d$.\\\n\n3. ", " $\\mathcal{E}(A^1)\\leq\\mathcal{E}(A)$, and equality holds if and only if $A^1=A$.\\\n\nIndeed,\n\n1. ", " This follows from the fact that the size of the fibers don’t change in the process, and that the fibers are disjoint. ", "$$|A|=\\sum_{x_2\\in{{\\mathbb{N}}}}{\\sum_{x_3\\in{{\\mathbb{N}}}}{\\ldots\\sum_{x_d\\in{{\\mathbb{N}}}}{|A_{(x_2,x_3,\\ldots,x_d)}|}}}\n =\\sum_{x_2\\in{{\\mathbb{N}}}}{\\sum_{x_3\\in{{\\mathbb{N}}}}{\\ldots\\sum_{x_d\\in{{\\mathbb{N}}}}{|A^1_{(x_2,x_3,\\ldots,x_d)}|}}}\n =|A^1|. ", "\\nonumber$$\n\n2. ", " For $j=1$ this is true since $$\\begin{aligned}\n (x_2,x_3,\\ldots,x_d)\\in\\Pi^1(A) \\Leftrightarrow \\exists ~\n a\\in{{\\mathbb{N}}}~such~that~(a,x_2,x_3,\\ldots,x_d)\\in A \\Leftrightarrow \\nonumber\\\\\n \\exists ~b\\in{{\\mathbb{N}}}~such~that~ (b,x_2,x_3,\\ldots,x_d)\\in A^1\n \\Leftrightarrow (x_2,x_3,\\ldots,x_d)\\in\\Pi^1(A^1), ~\\nonumber\\end{aligned}$$ and therefore $|\\Pi^1(A^1)|=|\\Pi^1(A)|$. For $2\\leq j\\leq d$, we assume for contradiction that, $|\\Pi^j(A^1)|> |\\Pi^j(A)|$. Then there exist $(x_1,x_2,\\ldots,x_{j-1},x_{j+1},\\ldots,x_d)\\in \\Pi^j(A^1)$ such that $$|\\Pi^j(A^1)_{(x_2,\\ldots,x_{j-1},x_{j+1},\\ldots,x_d)}|>\n |\\Pi^j(A)_{(x_2,\\ldots,x_{j-1},x_{j+1},\\ldots,x_d)}|. ", "\\nonumber$$ From the definition of $A^1$ there exists $m\\in{{\\mathbb{N}}}$ such that $$|\\Pi^j(A^1)_{(x_2,\\ldots,x_{j-1},x_{j+1},\\ldots,x_d)}|=|A^1_{(x_2,\\ldots,x_{j-1},m,x_{j+1},\\ldots,x_d)}|,\n \\nonumber$$ and since for every $k\\in{{\\mathbb{N}}}$ $$|A_{(x_2,\\ldots,x_{j-1},k,x_{j+1},\\ldots,x_d)}|\\leq\n |\\Pi^j(A)_{(x_2,\\ldots,x_{j-1},x_{j+1},\\ldots,x_d)}|. ", "\\nonumber$$ It follows that $$|A^1_{(x_2,\\ldots,x_{j-1},m,x_{j+1},\\ldots,x_d)}|>\n |A_{(x_2,\\ldots,x_{j-1},m,x_{j+1},\\ldots,x_d)}|,$$ which contradicts the fact that the size of fibers in $A$ and $A^1$ is the same.\\\n\n3. ", " By definition $$\\begin{aligned}\n \\mathcal{E}(A^1)&=\\sum_{x_2\\in{{\\mathbb{N}}}}{\\sum_{x_3\\in{{\\mathbb{N}}}}{\\ldots\\sum_{x_d\\in{{\\mathbb{N}}}}{~~\\sum_{x_1\\in\n A^1_{(x_2,x_3,\\ldots,x_d)}}{(x_1+x_2+\\ldots+x_d)}}}} \\nonumber\\\\\n &=\\sum_{x_2\\in{{\\mathbb{N}}}}{\\sum_{x_3\\in{{\\mathbb{N}}}}{\\ldots\\sum_{x_d\\in{{\\mathbb{N}}}}{\\left[|A^1_{(x_2,x_3,\\ldots,x_d)}|(x_2+x_3+\\ldots+x_d)+\\mathcal{E}(A^1_{(x_2,x_3,\\ldots,x_d)})\\right]}}}\n \\nonumber\\\\\n &=\\sum_{x_2\\in{{\\mathbb{N}}}}{\\sum_{x_3\\in{{\\mathbb{N}}}}{\\ldots\\sum_{x_d\\in{{\\mathbb{N}}}}{\\left[|A_{(x_2,x_3,\\ldots,x_d)}|(x_2+x_3+\\ldots+x_d)+\\mathcal{E}(A^1_{(x_2,x_3,\\ldots,x_d)})\\right]}}}\n \\nonumber\\\\\n &\\leq\\sum_{x_2\\in{{\\mathbb{N}}}}{\\sum_{x_3\\in{{\\mathbb{N}}}}{\\ldots\\sum_{x_d\\in{{\\mathbb{N}}}}{\\left[|A_{(x_2,x_3,\\ldots,x_d)}|(x_2+x_3+\\ldots+x_d)+\\mathcal{E}(A_{(x_2,x_3,\\ldots,x_d)})\\right]}}}\n \\nonumber\\\\\n &=\\mathcal{E}(A) \\nonumber\\\\\n \\end{aligned}$$ where the inequality is true since the energy of the $(x_2,x_3,\\ldots,x_d)$ fiber of $A^1$ is the one with least energy from all $(x_2,x_3,\\ldots,x_d)$ fibers of $A$. ", "In addition equality holds if and only if for every $(x_2,x_3,\\ldots,x_d)$ fiber of $A$ we have $\\mathcal{E}(A_{(x_2,x_3,\\ldots,x_d)})=\\mathcal{E}(A^1_{(x_2,x_3,\\ldots,x_d)})$ which is possible if and only if $A_{(x_2,x_3,\\ldots,x_d)}=A^1_{(x_2,x_3,\\ldots,x_d)}$, since $A^1$ fibers were chosen to be with minimal energy.", "\n\nRepeating the last procedure for the set $A^i$ with the $i+1^{\\mbox{th}}$ coordinate instead of the first one we obtain the sets $A^2,\\ldots,A^d$, with the same number of point, decreasing energy and decreasing size of projections. ", "Let $\\widetilde{A}_0\\equiv A$, and define by induction $\\widetilde{A}_{n+1}=\\widetilde{A}_n^d$ be the set generated from $\\widetilde{A}_n$ by repeating the last procedure. ", "It follows that sequence of sets $\\{\\widetilde{A}_n\\}_{n=0}^{\\infty}$ contains only finite number of sets. ", "Indeed since the energy of a set is an natural number, and the energy can only decrease as $n$ increases, there exist N such that for every $n\\geq N$ the energy is constant. ", "Using now property (3) it follows that $\\widetilde{A}_n=\\widetilde{A}_{n+1}$ for every $n\\geq N$ and therefore there is only finite number of sets in the sequence. ", "Let $\\widehat{A}$ be the limiting set of the sequence. ", "Note that the boundary of $\\widehat{A}$ is exactly $2\\sum_{i=1}^{d}{\\Pi^i\\big(\\widehat{A}\\big)}$, because otherwise one can decrease the energy. ", "Using the fact that the boundary of every set of size $n$ in $d$ dimensions is at least $C_0\\cdot\nn^{\\frac{d-1}{d}}$ for some positive constant $C_0$, see [@DP96], we get that there exist a positive constant $C$ and at least one $i_0\\in\\{1,2,\\ldots,d\\}$ such that $\\Pi^{i_0}\\big(\\widehat{A}\\big)\\geq C\\cdot n^{\\frac{d-1}{d}}$, and therefore $\\Pi^{i_0}(A)\\geq C_0n^{\\frac{d-1}{d}}$ for the original set $A$ too, as required.", "\n\nWe now turn to define the isoperimetric profile of a graph. ", "Let $\\{p(x,y)\\}_{x,y\\in V}$ be transition probabilities for an irreducible Markov chain on a countable state space V (we will think about this Markov chain as the random walk on a weighted graph $G=(V,E,C)~$, with $\\{x,y\\}\\in E$ if and only if $p(x,y)>0$ and for every $\\{x,y\\}\\in\nE$ we define the conductance $C(x,y)=p(x,y)$. For $S\\subset V$, the “boundary size” of S is measured by $|\\partial S|=\\sum_{s\\in\nS}{\\sum_{a\\in S^c}{p(s,a)}}$. We define $\\Phi_S$, the conductance of S, by $\\Phi_S:=\\frac{|\\partial S|}{|S|}$. Finally, define the isoperimetric profile of the graph G, with vertices V and conductances induced from the transition probabilities by: $$\\Phi(u)=\\inf\\{\\Phi_S:S\\subset V,~|S|\\leq u\\}.$$\n\nWe can now state Theorem 1 of [@MP08].", "\n\nLet $G=(V,E)$ be a graph with countable vertices and bounded degree. ", "Suppose that $0<\\gamma\\leq\\frac{1}{2}$ and $p(x,x)\\geq\\gamma$ for all $x\\in V$. If $$n\\geq\n1+\\frac{(1-\\gamma)^2}{\\gamma^2}\\int_{4}^{4/{{\\epsilon}}}{\\frac{4du}{u\\Phi^2(u)}},\n\\label{integral_condition}$$ then $$|p^n(x,y)|\\leq{{\\epsilon}}.$$ \\[MP\\_theorem\\]\n\nNext we will prove the following claim:\n\nLet $p_{{\\omega}}^n(x,y)$ be the probability that the random walk moves from $x$ to $y$ in $n$ steps in the environment ${{\\omega}}$. Then there exist positive constants $K_1,K_2$ depending only on $d$, and a natural number $N$ such that for every $n>N$ and every $x,y\\in{{\\mathcal{P}}}({{\\omega}})$ $$p_{{\\omega}}^{n}(x,y)\\leq\\frac{K_2}{(n-K_1)^{d/2}},~~~~~~P~a.s.$$ \\[bound\\_of\\_transitions\\]\n\nWe start by dealing with even steps of the Markov chain, and at the end extend the argument to the odd ones. ", "Since $p^2(x,x)=\\frac{1}{2d}$, we can use Theorem \\[MP\\_theorem\\] with $\\gamma=\\frac{1}{2d}$. Let ${{\\omega}}\\in{{\\Omega}}_0$ and $S\\subset{{\\mathcal{P}}}({{\\omega}})$ such that $|S|=n$. By Lemma \\[lem\\_volume\\_surface\\] there exists a positive constant $C$, such that at least one of the projections $\\{\\Pi^i(S)\\}_{i=1}^d$ satisfy $\\Pi^{i}(S)\\geq C\\cdot n^{\\frac{d-1}{d}}$. We will assume without loss of generality that this holds for $i=1$. We now look at the set $$\\widetilde{S}=\\big\\{(x_1,x_2,\\ldots,x_d):~(x_2,\\ldots,x_d)\\in\\Pi^1(S),~~x_1=\\max\\{a:(a,x_2,x_3,\\ldots,x_d)\\in\nS\\}\\big\\}.$$ We note that $|\\widetilde{S}|=|\\Pi^1(s)|\\geq C n^{(d-1)/d}$. In addition since $|\\partial S|$ equals in our case to $\\frac{1}{2d}$ times the number of edges $e\\in E$ with one end point in $S$ and the other in $S^c$, then $|\\partial S|\\geq \\frac{1}{2d}|\\widetilde{S}|$. This is true since every element in $\\widetilde{S}$ contributes at least one edge to the boundary. ", "Using these two properties it follows that there exists a positive constant $C_0$ such that $$\\Phi(u)\\geq C_0\\frac{1}{u^{1/d}}, \\label{Phi_estimation}$$ and therefore $$\\begin{aligned}\n1+(2d-1)^2\\int_{4}^{4/{{\\epsilon}}}{\\frac{4du}{u\\Phi^2(u)}} & \\leq\n1+(2d-1)^2\\int_{4}^{4/{{\\epsilon}}}{\\frac{4u^{\\frac{2}{d}-1}du}{C_0^2}} \\nonumber\\\\\n&\\leq \\left\\lceil\n1-\\frac{2d(2d-1)^2}{c_0^2}4^{\\frac{2}{d}}+\\frac{2d(2d-1)^2}{c_0^2}4^{\\frac{2}{d}}{{\\epsilon}}^{-\\frac{2}{d}}\n\\right\\rceil . ", "\\nonumber \\label{isoperimetric}\n\\end{aligned}$$ Notice that $1-\\frac{2d(2d-1)^2}{c_0^2}4^{\\frac{2}{d}}$ is negative for all but a finite number of dimensions, and therefore we can find a natural number $\\widetilde{K}_1(d)$ such that the last term in is less than or equal to $$n({{\\epsilon}})\\equiv\\lceil\n\\widetilde{K}_1+\\widetilde{K}_2{{\\epsilon}}^{-\\frac{2}{d}}\\rceil,$$ where $\\widetilde{K}_2=\\widetilde{K}_2(d)=\\frac{2d(2d-1)^2}{c_0^2}4^{\\frac{2}{d}}$. It therefore follows that $${{\\epsilon}}\\leq\n\\left(\\frac{n({{\\epsilon}})-\\widetilde{K}_1-1}{\\widetilde{K}_2}\\right)^{-\\frac{d}{2}}.$$\n\nLet $K_2=(\\widetilde{K}_2)^{-\\frac{d}{2}}$, since the condition in Theorem \\[MP\\_theorem\\] is fulfilled, for $P$ almost every environment ${{\\omega}}$, for every $n>N$ and every $x,y\\in{{\\mathcal{P}}}({{\\omega}})$ $$p_{{\\omega}}^{2n}(x,y)\\leq\n\\frac{K_2}{(2n-\\widetilde{K}_1-1)^{\\frac{d}{2}}}.$$\n\nMoving to deal with transition probabilities for odd times, if $n>N+1$ we have for $P$ almost every environment ${{\\omega}}$ $$\\begin{aligned}\np^{2n+1}_{{\\omega}}(x,y)&=\\sum_{z\\in{{\\mathcal{P}}}({{\\omega}})}{p_{{\\omega}}(x,z)p^{2n}_{{\\omega}}(z,y)}\\nonumber\\\\\n&\\leq \\sum_{z\\in{{\\mathcal{P}}}({{\\omega}})}{p_{{\\omega}}(x,z)\\frac{K_2}{(2n-\\widetilde{K}_1-1)^\\frac{d}{2}}}\\\\\n&= \\frac{K_2}{(2n+1-\\widetilde{K}_1-2)^\\frac{d}{2}}.", "\n\\end{aligned}$$ Taking $K_1=\\widetilde{K}_1+2$ we get the desired inequality both for even times and odd ones.", "\n\nWe are now ready to prove Theorem \\[tran\\_recu3\\].", "\n\nSince our graph is connected, it is enough to show that $$\\sum_{n=0}^{\\infty}{p^n(0,0)}<\\infty.$$ Using claim \\[bound\\_of\\_transitions\\], we get that for $P$ almost every environment ${{\\omega}}\\in{{\\Omega}}_0$ $$\\sum_{n=0}^{\\infty}{p_{{\\omega}}^n(0,0)}\\leq\\sum_{n=0}^{N-1}{p_{{\\omega}}^n(0,0)}+\\sum_{n=N}^{\\infty}{\\frac{2K_2}{(2n-K_1)^{\\frac{d}{2}}}}<\\infty.$$\n\nAsymptotic behavior of the random walk\n======================================\n\nIn this section we prove asymptotic behavior of ${{\\mathbb{E}}}(\\|X_n\\|)$. This will be used in section 10 to prove the high dimensional Central Limit Theorem. ", "Therefore we assume here the additional assumption, assumption \\[assumption3\\]. ", "The estimation follows closely [@Ba03] with the following changes:\n\n- The minor change is that we work in discrete time setting and not in continuous time.\\\n\n- The major change is that the average variance of the distance at the $n^{\\mbox{th}}$ step of the random walk is not bounded by 1 as in the percolation case. ", "Nevertheless we can show that if we assume in addition assumption \\[assumption3\\], it is still bounded.", "\n\nOther than that problem, in which we deal in part $(3)$ of Theorem \\[asymptotic\\_X\\_n\\], the rest of the proof doesn’t contain new ideas and follows [@Ba03]\n\nAssuming assumption \\[assumption3\\], there exists a random variable $c:{{\\Omega}}_0\\rightarrow [0,\\infty]$ which is finite almost surely such that for $P$ almost every ${{\\omega}}\\in{{\\Omega}}_0$ $${{\\mathbb{E}}}_{{\\omega}}(\\|X_n\\|)\\leq c\\sqrt{n}~~~\\forall n\\in{{\\mathbb{N}}}.$$ \\[asymptotic\\_X\\_n\\]\n\nWe begin with a few definitions\n\nFix ${{\\omega}}\\in{{\\Omega}}_0$. For $n\\in{{\\mathbb{N}}}$ we denote $p^n(x,y)=P_{{\\omega}}(X_n=y|X_0=x)$ and introduce the following functions, with the understanding that $0\\cdot\\log(0)=0$:\n\n1. ", " $g_n:{{\\mathcal{P}}}({{\\omega}})\\rightarrow{{\\mathbb{R}}}$, given by $$g_n(x)=\\frac{1}{2}\\left(p^n(0,x)+p^{n-1}(0,x)\\right).$$\n\n2. ", " We define $M:{{\\mathbb{N}}}\\rightarrow{{\\mathbb{R}}}^+$ by $M(0)=0$ and for $n>0$ by: $$M(n)=\\frac{1}{2}{{\\mathbb{E}}}_{{\\omega}}(\\|X_n\\|+\\|X_{n-1}\\|):=\\sum_{y\\in{{\\mathcal{P}}}({{\\omega}})}{\\|y\\|g_n(y)}.$$\n\n3. ", " We define $Q:{{\\mathbb{N}}}\\rightarrow{{\\mathbb{R}}}^+$ by $Q(0)=0$ and for $n>0$ by: $$Q(n)=-\\sum_{y\\in{{\\mathcal{P}}}({{\\omega}})}{g_n(y)\\log(g_n(y))},$$ i.e. $Q$ is the entropy of $g_n$.\n\nIn order to prove Theorem \\[asymptotic\\_X\\_n\\], we will prove some inequalities introduced in the following proposition:\n\nThere exists $N=N({{\\omega}})\\in{{\\mathbb{N}}}$ and constants $c_1,c_2,c_3,K_1<\\infty$ such that for every $n>N$ we have\n\n1. ", " $$Q(n)\\geq c_1+\\frac{d}{2}\\log{(n-K_1)}, \\label{distance_prop_1}$$\n\n2. ", " $$M(n)\\geq c_2\\cdot e^{\\frac{Q(n)}{d}}, \\label{distance_prop_2}$$\n\n3. ", " $$\\sum_{x\\in{{\\mathcal{P}}}({{\\omega}})}{\\sum_{y\\in{{\\mathcal{P}}}({{\\omega}})}{{{\\mathbbm{1}}}_{\\{y\\in\n N_x({{\\omega}})\\}}{(g_n(x)+g_n(y))\\|x-y\\|^2}}}<\\infty,\n \\label{distance_prop_3}$$\n\n4. ", " $$(M(n+1)-M(n))^2\\leq c_3(Q(n+1)-Q(n)). ", "\\label{distance_prop_4}$$\n\nWe note that we don’t have any estimation on the tail of $N({{\\omega}})$.\\\n\n$~$\\\n\n1. ", " From the definition of $Q(n)$ we have that $$Q(n)\\geq \\inf_{y\\in{{\\mathcal{P}}}({{\\omega}})}(-\\log(g_n(y)))=-\\sup_{y\\in{{\\mathcal{P}}}({{\\omega}})}{(\\log(g_n(y)))}.", "\n \\nonumber$$ Using now Claim \\[bound\\_of\\_transitions\\], for sufficiently large $n$ we have $\\forall y\\in{{\\mathcal{P}}}({{\\omega}})$ that $g_n(y)\\leq \\frac{K_2}{(n-K_1)^{\\frac{d}{2}}}$ and therefore $$Q(n)\\geq -\\log\\left(\n \\frac{K_2}{(n-K_1)^\\frac{d}{2}}\\right)=-\\log(K_2)+\\frac{d}{2}\\log(n-K_1).$$ Taking $c_1=-\\log(2K_2)$ we get the desired inequality.\\\n\n2. ", " Let $D_n=B_{2^n}(0)\\backslash B_{2^{n-1}}(0)$ for $n>0$ and $D(0)=\\{0\\}$, where $B_n(0)=\\{x\\in{{\\mathbb{Z}}}^d ~:~|x|\\leq n\\}$. Then for $0\\leq a\\leq 2$ we have: $$\\sum_{y\\in{{\\mathcal{P}}}({{\\omega}})}{e^{-a\\|y\\|}} \\leq \\sum_{n=0}^{\\infty}{\\sum_{y\\in\n D_n}{e^{-a\\cdot 2^n}}}\\leq \\sum_{n=0}^{\\infty}{e^{-a\\cdot 2^n}\\cdot\n c_{2.1}\\cdot 2^{nd}}\\leq c_{2.2}\\cdot a^{-d},\n \\label{distance_inequality_1}$$ where $c_{2.2}=c_{2.2}(d)$ depends on d. Indeed, the first inequality is true since $a\\leq 2$, the second inequality follows from the fact that the set of points in ${{\\mathcal{P}}}({{\\omega}})$ with distance greater than $2^{n-1}$ and less than $2^n$ is bounded by the number of points in ${{\\mathbb{Z}}}^d$ with those properties, which is less than a constant times $2^{nd}$. The proof of the last inequality follows by separating the series into two parts, up to some $n_0$ and starting from $n_0$, and then bounding the second one by a geometric series. ", "The proof of it can be found in the Appendix.", "\n\n Since for every $u>0$ and every $\\lambda\\in{{\\mathbb{R}}}$ we have $u(\\log(u)+\\lambda)\\geq -e^{-1-\\lambda}$, by taking $\\lambda=a\\|y\\|+b$ with $a\\leq 2$ and $u=g_n(y)$ we get $$\\label{eq:one_more}\n \\begin{aligned}\n -Q(n)+aM(n)+b&=\\sum_{y\\in{{\\mathcal{P}}}({{\\omega}})}{g_n(y)\\left(\\log(g_n(y))+a\\|y\\|+b\\right)}\\\\\n &\\geq-\\sum_{y\\in{{\\mathcal{P}}}({{\\omega}})}{e^{-1-a\\|y\\|-b}=-e^{-1-b}\\sum_{y\\in{{\\mathcal{P}}}({{\\omega}})}{e^{-a\\|y\\|}}}.", "\n \\end{aligned}$$\n\n Note that we actually used the last inequality only for those $y\\in{{\\mathcal{P}}}({{\\omega}})$ such that $g_n(y)>0$, and for $y\\in{{\\mathcal{P}}}({{\\omega}})$ such that $g_n(y)=0$ we used the fact that $0\\geq -e^{-1-a\\|y\\|-b}$. Combining and we get that $$-Q(n)+aM(n)+b\\geq -e^{-1-b} c_{2.2} a^{-d}.", "\n \\label{ditance_inequality_2.1}$$ But for sufficiently large $n$ we have $$\\begin{aligned}\n M(n)&=0\\cdot g_n(0)+\\sum_{y\\in{{\\mathcal{P}}}({{\\omega}}),y\\neq 0}{d(0,y)g_n(y)}\\\\\n \\nonumber &\\geq \\sum_{y\\in{{\\mathcal{P}}}({{\\omega}}),y\\neq 0}{g_n(y)}=1-g_n(0)\\geq\n \\frac{1}{2}. ", "\\label{distance_inequality_2.2}\n \\end{aligned}$$ Taking now $a=\\frac{1}{M(n)}$ and $b=d\\cdot \\log\\left(M(n)\\right)$, by (and since by we have $a\\leq 2$) it follows that $$-Q(n)+1+d\\cdot\\log(M(n))\\geq -e^{-1} c_{2.2}=-c_{2.3}. ", "\\nonumber$$ Note that $c_{2.3}=c_{2.3}(d)$ also depend on $d$. Rearranging the last inequality we get that there exists a constant $c_2=c_2(d)$ such that $$M(n)\\geq c_2\\cdot e^\\frac{Q(n)}{d}. ", "\\nonumber$$\n\n3. ", " We start by rearranging the sum as $$\\begin{aligned}\n \\sum_{x,y\\in{{\\mathcal{P}}}({{\\omega}})}{{{\\mathbbm{1}}}_{\\{y\\in\n N_x({{\\omega}})\\}}(g_n(x)+g_n(y))\\|x-y\\|^2}\n &=2\\sum_{x\\in{{\\mathcal{P}}}({{\\omega}})}{g_n(x)\\sum_{y\\in N_x({{\\omega}})}{\\|x-y\\|^2}}\\\\\n &= 2\\sum_{e\\in\\{\\pm\n e_i\\}_{i=1}^d}{\\sum_{x\\in{{\\mathcal{P}}}({{\\omega}})}{g_n(x)f_e^2({{\\theta}}^{x}{{\\omega}})}}\\\\\n &=2\\sum_{e\\in\\{\\pm e_i\\}_{i=1}^d}{\\left(E_{{\\omega}}(f_e^2\\circ\n {{\\theta}}^{X_n})+E_{{\\omega}}(f_e^2\\circ {{\\theta}}^{X_{n-1}})\\right)}. ", "\\nonumber\n \\end{aligned}$$\n\n In order to show that this sum is finite, we will use a theorem taken from [@NS94]. ", "Before we can state the theorem we need the following definitions:\n\n Given a countable group $\\Gamma$ we define $l^1(\\Gamma)=\\{\\mu=\\sum_{\\gamma\\in\\Gamma}\\mu(\\gamma)\\gamma:\\sum_{\\gamma\\in\\Gamma}|\\mu(\\gamma)|<\\infty\\}$. Let $(X,\\mathcal{B},m)$ be a standard Lebesgue probability space, and assume $\\Gamma$ acts on $X$ by measurable automorphisms preserving the probability measure $m$. This action induces a representation of $\\Gamma$ by isometries on the $L^p(X)$ spaces, $1\\leq p\\leq \\infty$, and this representation can be extended to $l^1(\\Gamma)$ by $(\\mu\n f)(x)=\\sum_{\\gamma\\in\\Gamma}{\\mu(\\gamma)f(\\gamma^{-1}x)}$. Let $\\mathcal{B}_1=\\{A\\in\\mathcal{B}:m(\\gamma A\\bigtriangleup A)=0~\\forall\n \\gamma\\in\\Gamma\\}$ denote the sub ${{\\sigma}}$-algebra of invariant sets, and denote by $E_1$ the conditional expectation with respect to $\\mathcal{B}_1$. We call a sequence $\\nu_n\\in l^1(\\Gamma)$ a pointwise ergodic sequence in $L^p$ if, for any action of $\\Gamma$ on a Lebesgue space X which preserves a probability measure and for every $f\\in L^p(X)$, $\\nu_nf(x)\\rightarrow E_1f(x)$ for almost all $x\\in X$, and in the norm of $L^p(X)$. If $\\Gamma$ is finitely generated, let S be a finite generating symmetric set. ", "S induces a length function on $\\Gamma$, given by $|\\gamma|=|\\gamma|_S=\\min\\{n:\\gamma=s_1s_2\\ldots s_n,s_i\\in S\\}$, and $|e|=0$. We can therefore define the following sequences:\n\n $~$\\\n\n 1. ", " $\\tau_n=(\\# S_n)^{-1}\\sum_{w\\in S_n} w$, where $S_n=\\{w:|w|=n\\}$.\n\n 2. ", " $\\tau '_n=\\frac{1}{2}(\\tau_n+\\tau_{n+1})$.\n\n 3. ", " $\\mu_n=\\frac{1}{n+1}\\sum_{k=0}^{n}{\\tau_k}$.\n\n 4. ", " $\\beta_n=(\\# B_n)^{-1}\\sum_{w\\in B_n}w$, where $B_n=\\{w:|w|\\leq\n n\\}$.\n\n We can now state the theorem:\n\n \\[Nevo, Stein 94\\] Consider the free group $F_r$, $r\\geq 2$. Then:\n\n 1. ", " The sequence $\\mu_n$ is a pointwise ergodic sequence in $L^p$, for all $1\\leq p< \\infty$.\n\n 2. ", " The sequence $\\tau '_n$ is a pointwise ergodic sequence in $L^p$, for $1<p<\\infty$.\n\n 3. ", " $\\tau_{2n}$ converges to an operator of conditional expectation with respect to an $F_r$-invariant sub ${{\\sigma}}$-algebra. ", "$\\beta_{2n}$ converges to the operator $E_1+((r-1)/r)E$, where E is a projection disjoint from $E_1$. Given $f\\in L^p(X)$, $1<p<\\infty$, the convergence is pointwise almost everywhere, and in the $L^p$ norm.", "\n\n \\[Birkhoff-generalization\\]\n\n We actually only need the second part of Theorem \\[Birkhoff-generalization\\]. ", "Taking $S=\\{{{\\sigma}}_{\\pm\n e_i}\\}_{i=1}^{d}$, we get that $$2\\sum_{e\\in\\{\\pm e_i\\}_{i=1}^d}{\\left(E_{{\\omega}}(f_e^2\\circ\n {{\\theta}}^{X_n})+E_{{\\omega}}(f_e^2\\circ {{\\theta}}^{X_{n-1}})\\right)} \\leq 4\\sum_{e\\in\\{\\pm e_i\\}_{i=1}^d}{\\tau_n'(f_e^2)}.\\nonumber$$ Using the additional assumption, we get that there exists $1<p<\\infty$ such that for every coordinate direction $e$, $f_e^2\\in\n L^p({{\\Omega}}_0)$. Therefore by Theorem \\[Birkhoff-generalization\\] $$\\lim_{n\\rightarrow\\infty}{4\\sum_{e\\in\\{\\pm\n e_i\\}_{i=1}^d}{\\tau_n'(f_e^2)}}=E_1\\left(4\\sum_{e\\in\\{\\pm\n e_i\\}_{i=1}^d}{f_e^2}\\right), \\nonumber$$ exists. ", "In addition, since $P$ is ergodic with respect to ${{\\sigma}}_e$ for every coordinate direction $e$, there exists a constant $C$ such that $4\\sum_{e\\in\\{\\pm e_i\\}_{i=1}^d}{E_1(f_e^2)}=C$ $P$-almost surely. ", "Consequently, the original sequence converges to $C$ $P$-almost surely, and therefore in particular it is $P$-almost surely bounded.", "\n\n4. ", " $$M(n+1)-M(n)=\\sum_{y\\in{{\\mathcal{P}}}({{\\omega}})}{(g_{n+1}(y)-g_n(y))\\|y\\|}. ", "\\nonumber$$\n\n Using the discrete Gauss Green formula, this term equals to $$\\label{Green_formula}\n -\\frac{1}{4d}\\sum_{x,y\\in{{\\mathcal{P}}}({{\\omega}})}{{{\\mathbbm{1}}}_{\\{y\\in\n N_x({{\\omega}})\\}}(\\|y\\|-\\|x\\|)(g_n(y)-g_n(x))}.$$ Indeed,rearranging the sums we get that $\\sum_{y\\in{{\\mathcal{P}}}({{\\omega}})}{(g_{n+1}(y)-g_n(y))\\|y\\|}$ equals to $$-\\frac{1}{4d}\\left[2d\\sum_{y\\in{{\\mathcal{P}}}({{\\omega}})}{\\|y\\|g_n(y)}+2d\\sum_{x\\in{{\\mathcal{P}}}({{\\omega}})}{\\|x\\|g_n(x)}\\right.", "\n \\left.-2d\\sum_{y\\in{{\\mathcal{P}}}({{\\omega}})}{\\|y\\|g_{n+1}(y)}-2d\\sum_{x\\in{{\\mathcal{P}}}({{\\omega}})}{\\|x\\|g_{n+1}(x)}\\right].", "\n \\nonumber$$ Since all sums are finite and for every point in $x\\in{{\\mathcal{P}}}({{\\omega}})$ we have $|N_x({{\\omega}})|=2d<\\infty$ we get that the last term is equal to $$\\begin{aligned}\n -\\frac{1}{4d}\\left[\\sum_{y\\in{{\\mathcal{P}}}({{\\omega}})}{\\|y\\|g_n(y)\\sum_{x\\in{{\\mathcal{P}}}({{\\omega}})}{{{\\mathbbm{1}}}_{y\\in\n N_x({{\\omega}})}}}+\\sum_{x\\in{{\\mathcal{P}}}({{\\omega}})}{\\|x\\|g_n(x)\\sum_{y\\in{{\\mathcal{P}}}({{\\omega}})}{{{\\mathbbm{1}}}_{y\\in\n N_x({{\\omega}})}}} \\right.\\nonumber\\\\\n \\left.- \\sum_{y\\in{{\\mathcal{P}}}({{\\omega}})}{\\|y\\|\\sum_{x\\in{{\\mathcal{P}}}({{\\omega}})}{{{\\mathbbm{1}}}_{y\\in\n N_x({{\\omega}})}g_n(x)}}-\\sum_{x\\in{{\\mathcal{P}}}({{\\omega}})}{\\|x\\|\\sum_{y\\in{{\\mathcal{P}}}({{\\omega}})}{{{\\mathbbm{1}}}_{y\\in\n N_x({{\\omega}})}g_n(y)}}\\right].\\nonumber\n \\end{aligned}$$ But again all sums are finite and therefore we can change the order of summation getting the following presentation $$\\begin{aligned}\n &-\\frac{1}{4d}\\sum_{x,y\\in{{\\mathcal{P}}}({{\\omega}})}{\\left[{{\\mathbbm{1}}}_{y\\in\n N_x({{\\omega}})}\\|y\\|g_n(y)-{{\\mathbbm{1}}}_{y\\in N_x({{\\omega}})}\\|x\\|g_n(y)-{{\\mathbbm{1}}}_{y\\in\n N_x({{\\omega}})}\\|y\\|g_n(x)+{{\\mathbbm{1}}}_{y\\in N_x({{\\omega}})}\\|x\\|g_n(x)\\right]}\n \\nonumber\\\\\n =&-\\frac{1}{4d}\\sum_{x,y\\in{{\\mathcal{P}}}({{\\omega}})}{{{\\mathbbm{1}}}_{\\{y\\in\n N_x({{\\omega}})\\}}(\\|y\\|-\\|x\\|)(g_n(y)-g_n(x))}.", "\n \\end{aligned}$$ Using and the triangle inequality we get that $M(n+1)-M(n)$ is less or equal than $$\\frac{1}{4d}\\sum_{x,y\\in{{\\mathcal{P}}}({{\\omega}})}{{{\\mathbbm{1}}}_{\\{y\\in\n N_x({{\\omega}})\\}}\\|x-y\\|\\left|g_n(y)-g_n(x)\\right|}.\\nonumber$$ Therefore by the Cauchy Schwartz inequality $$\\begin{aligned}\n M(n+1)-M(n)\\leq\n \\frac{1}{4d}&\\left(\\sum_{x,y\\in{{\\mathcal{P}}}({{\\omega}})}{{{\\mathbbm{1}}}_{\\{y\\in\n N_x({{\\omega}})\\}}(g_n(x)+g_n(y))\\|x-y\\|^2}\\right)^\\frac{1}{2}\\nonumber\\\\\n \\cdot &\\left(\\sum_{x,y\\in{{\\mathcal{P}}}({{\\omega}})}{{{\\mathbbm{1}}}_{\\{y\\in\n N_x({{\\omega}})\\}}\\frac{(g_n(y)-g_n(x))^2}{g_n(y)+g_n(x)}}\\right)^\\frac{1}{2}.\\nonumber\n \\label{distance_inequality_3.1}\n \\end{aligned}$$\n\n The first sum here is exactly the same sum from (\\[distance\\_prop\\_3\\]) and therefore is finite, so there exists a positive constant $c_{3.1}=c_{3.1}(d)$ such that $M(n+1)-M(n)$ is less or equal to $$c_{3.1}\\left(\\sum_{x,y\\in{{\\mathcal{P}}}({{\\omega}})}{{{\\mathbbm{1}}}_{\\{y\\in\n N_x({{\\omega}})\\}}\\frac{(g_n(y)-g_n(x))^2}{g_n(y)+g_n(x)}}\\right)^\\frac{1}{2}.", "\n \\nonumber$$ Using the fact that for every $u,v>0$ $$\\frac{(u-v)^2}{u+v}\\leq(u-v)\\left(\\log(u)-\\log(v)\\right). ", "\\nonumber$$ We get that $M(n+1)-M(n)$ is less or equal than $$c_{3.1}\\left(\\sum_{x,y\\in{{\\mathcal{P}}}({{\\omega}})}{{{\\mathbbm{1}}}_{\\{y\\in\n N_x({{\\omega}})\\}}\\Big(g_n(y)-g_n(x)\\Big)\\Big(\\log(g_n(y))-\\log(g_n(x))\\Big)}\\right)^\\frac{1}{2}.", "\n \\nonumber$$ Using the discrete Gauss Green formula in the other direction, the last term equals to $$\\sqrt{4d}c_{3.1}\\left(-\\sum_{y\\in{{\\mathcal{P}}}({{\\omega}})}{\\Big(\\log(g_n(y))+1\\Big)\\Big(g_{n+1}(y)-g_n(y)\\Big)}\\right)^\\frac{1}{2}.", "\n \\nonumber$$ Since $1-x+\\log(x)\\leq 0$ for all $x>0$ we get that the last term is less or euqal to $$\\sqrt{4d}c_{3.1}\\left(-\\sum_{y\\in{{\\mathcal{P}}}({{\\omega}})}{\\Big(g_{n+1}(y)-g_n(y)\\Big)\\log(g_n(y))+g_{n+1}(y)\\log\\left(\\frac{g_{n+1}(y)}{g_n(y)}\\right)}\\right)^\\frac{1}{2}.\\nonumber$$ But this is exactly $$\\sqrt{4d}c_{3.1}\\Big(Q(n+1)-Q(n)\\Big)^\\frac{1}{2}. ", "\\nonumber$$ By taking $c_3=(\\sqrt{4d}c_{3.1})^2$ gives the desired inequality.", "\n\nLet $R(n):{{\\mathbb{N}}}\\rightarrow{{\\mathbb{R}}}$ be defined by $$R(n)=\\frac{1}{d}\\Big(Q(n)-c_1-\\frac{d}{2}\\log(n-K_1)\\Big),$$ for $n>\\lceil K_1\\rceil+1$ and $R(n)=0$ for $n\\leq\\lceil\nK_1\\rceil+1$. By for sufficiently large $n$ we have $$M(n)\\geq c_2\\cdot e^\\frac{Q(n)}{d}=c_2\\cdot\ne^{R(n)+\\frac{c_1}{d}+\\frac{1}{2}\\log(n-K_1)}=c_{4.1}e^{R(n)}\\sqrt{n-K_1}.", "\n\\label{distance_inequality_last1}$$\n\nOn the other hand, let $N\\in{{\\mathbb{N}}}$ be such that for all $n>N$ inequalities (\\[distance\\_prop\\_1\\]-\\[distance\\_prop\\_4\\]) hold, then for every $n>N$ we have (set $c_{4.3}=\\sqrt{c_3}$) $$\\begin{aligned}\nM(n) & = \\sum_{k=1}^{N}{M(k)-M(k-1)}+\\sum_{k=N+1}^{n}{M(k)-M(k-1)}\n\\nonumber \\\\\n& \\leq c_{4.2}+c_{4.3}\\cdot\n\\sum_{k=N+1}^{n}{\\Big(Q(k)-Q(k-1)\\Big)^\\frac{1}{2}} \\nonumber \\\\\n& =\nc_{4.2}+c_{4.3}\\sqrt{d}\\sum_{k=N+1}^{n}{\\left(R(k)-R(k-1)+\\frac{1}{2}\\log\\left(\\frac{k-K_1}{k-1-K_1}\\right)\\right)^{\\frac{1}{2}}}.", "\n\\nonumber\n\\end{aligned}$$ Using the inequality $(a+b)^\\frac{1}{2}\\leq\nb^\\frac{1}{2}+\\frac{a}{(2b)^\\frac{1}{2}}$, we find that this is less than or equal to $$c_{4.2}+c_{4.3}\\sum_{k=N+1}^{n}{\\left[\\frac{1}{\\sqrt{2}}\\log^\\frac{1}{2}\\left(\\frac{k-K_1}{k-1-K_1}\\right)+\n\\frac{R(k)-R(k-1)}{\\log^\\frac{1}{2}\\left(\\frac{k-K_1}{k-1-K_1}\\right)}\\right]},\n\\nonumber$$ which can be written (using discrete integration by parts) as $$\\begin{aligned}\n&c_{4.2}+c_{4.3}\\sum_{k=N+1}{n}{\\frac{1}{\\sqrt{2}}\\log^\\frac{1}{2}\\left(\\frac{k-K_1}{k-1-K_1}\\right)}+\nc_{4.3}\\sum_{k=N+1}^{n}{\\left[\\frac{R(k)}{\\log^\\frac{1}{2}\\left(\\frac{k+1-K_1}{k-K_1}\\right)}-\\frac{R(k-1)}{\\log^\\frac{1}{2}\\left(\\frac{k-K_1}{k-1-K_1}\\right)}\\right]}\n\\nonumber\\\\\n&-c_{4.3}\\sum_{n=N+1}^{n}{R(k)\\left[\\frac{1}{\\log^\\frac{1}{2}\\left(\\frac{k+1-K_1}{k-K_1}\\right)}-\\frac{1}{\\log^\\frac{1}{2}\\left(\\frac{k-K_1}{k-1-K_1}\\right)}\\right]}.", "\n\\nonumber\n\\end{aligned}$$ Since holds $R(k)$ is non negative and therefore the last sum is positive. ", "Consequently we get $$\\label{distance_long_calc_1}\n\\begin{aligned}\nM(n)\\leq\nc_{4.2}&+c_{4.3}\\sum_{k=N+1}^{n}{\\frac{1}{\\sqrt{2}}\\log^\\frac{1}{2}\\left(\\frac{k-K_1}{k-1-K_1}\\right)}\\\\\n&+\nc_{4.3}\\sum_{k=N+1}^{n}{\\left[\\frac{R(k)}{\\log^\\frac{1}{2}\\left(\\frac{k+1-K_1}{k-K_1}\\right)}-\\frac{R(k-1)}{\\log^\\frac{1}{2}\\left(\\frac{k-K_1}{k-1-K_1}\\right)}\\right]}.", "\n\\end{aligned}$$ Using the fact that $$\\log\\left(\\frac{k-K_1}{k-1-K_1}\\right)=\\log\\left(1+\\frac{1}{k-1-K_1}\\right)<\\frac{1}{k-1-K_1}.", "\n\\nonumber$$ The first sum in is less than $$\\sum_{k=N+1}^{n}{\\frac{1}{(k-1-K_1)^\\frac{1}{2}}}\\leq\nc_{4.4}\\sqrt{n-K_1}. ", "\\nonumber$$ Therefore we find that $$\\begin{aligned}\nM(n) & \\leq c_{4.2}+c_{4.3} c_{4.4}\\sqrt{n-K_1}+c_{4.3}\n\\sum_{k=N+1}^{n}{\\left[\\frac{R(k)}{\\log^\\frac{1}{2}\\left(\\frac{k+1-K_1}{k-K_1}\\right)}-\\frac{R(k-1)}{\\log^\\frac{1}{2}\\left(\\frac{k-K_1}{k-1-K_1}\\right)}\\right]}\n\\nonumber\\\\\n& = c_{4.2}+c_{4.3}\nc_{4.4}\\sqrt{n-K_1}+c_{4.3}\\left[\\frac{R(n)}{\\log^\\frac{1}{2}\\left(\\frac{n+1-K_1}{n-K_1}\\right)}-\\frac{R(N+1)}{\\log^\\frac{1}{2}\\left(\\frac{N+1-K_1}{N-K_1}\\right)}\\right]\n\\nonumber\\\\\n& \\leq c_{4.2}+c_{4.3} c_{4.4}\\sqrt{n-K_1}+c_{4.3}\n\\frac{R(n)}{\\log^\\frac{1}{2}\\left(\\frac{n+1-K_1}{n-K_1}\\right)}\n\\nonumber\\\\\n& \\leq c_{4.2}+c_{4.3} c_{4.4}\\sqrt{n-K_1}+c_{4.3}\\cdot\nc_{4.5} R(n)\\sqrt{n-K_1}. ", "\\nonumber\n\\end{aligned}$$ We can thus find a constant $c_{4.6}$ such that for all sufficiently large $n$ $$M(n)\\leq c_{4.6}[1+R(n)]\\sqrt{n-K_1}.", "\n\\label{distance_inequality_last2}$$ So by and we have that for sufficiently large $n$ $$c_{4.1}e^{R(n)}\\sqrt{n-K_1}\\leq M(n)\\leq c_{4.6}[1+R(n)]\\sqrt{n-K_1}.", "\n\\nonumber$$ It follows that $R(n)$ must be a bounded function, and therefore we can find constants $c_{4.7},c_{4.8}$ such that for sufficiently large n $$c_{4.7}\\sqrt{n-K_1} \\leq M(n) \\leq c_{4.8}\\sqrt{n-K_1}. ", "\\nonumber$$ Consequently, since $$M(n)=\\frac{1}{2}\\Big[E_{{\\omega}}(\\|X_n\\|)+E_{{\\omega}}(\\|X_{n-1}\\|) \\nonumber\\Big],$$ it follows that there exists a constant $c>0$ such that for $P$ almost every ${{\\omega}}\\in{{\\Omega}}_0$ $$E_{{\\omega}}(\\|X_n\\|)\\leq c\\sqrt{n}~~~~\\forall n\\in{{\\mathbb{N}}}. ", "\\nonumber$$\n\nCorrector - Construction and harmonicity\n========================================\n\nIn this section, we adapt the construction presented in [@BB06] (which in turn adapts the construction of Kipnis and Varadhan [@KV86]) into our analysis.", "\n\nWe start with the following observation concerning the Markov chain “on environments”.", "\n\nFor every bounded measurable function $f:{{\\Omega}}_0\\rightarrow {{\\mathbb{R}}}$ and every $x\\in N_0({{\\omega}})$ we have $${{\\mathbb{E}}}_P\\left[(f\\circ {{\\theta}}_x){{\\mathbbm{1}}}_{\\{x\\in\nN_0({{\\omega}})\\}}\\right]={{\\mathbb{E}}}_P[f{{\\mathbbm{1}}}_{\\{-x\\in N_0({{\\omega}})\\}}].", "\n\\label{lem_chain_environments}$$ As a consequence, $P$ is reversible and, in particular, stationary for the Markov kernel $\\Lambda$ defined in (\\[Lambda\\]).", "\n\nWe will first prove (\\[lem\\_chain\\_environments\\]). ", "Up to the factor ${{\\mathbb{P}}}({{\\Omega}}_0)$, we need to show that $${{\\mathbb{E}}}_Q[f\\circ{{\\theta}}_x{{\\mathbbm{1}}}_{{{\\Omega}}_0}{{\\mathbbm{1}}}_{\\{x\\in\nN_0({{\\omega}})\\}}]={{\\mathbb{E}}}_Q[f{{\\mathbbm{1}}}_{{{\\Omega}}_0}{{\\mathbbm{1}}}_{\\{-x\\in N_0({{\\omega}})\\}}].", "\n\\label{lem_chain_environments2}$$ This will follow from the fact that ${{\\mathbbm{1}}}_{\\{x\\in\nN_0({{\\omega}})\\}}{{\\mathbbm{1}}}_{{{\\Omega}}_0}=\\left({{\\mathbbm{1}}}_{\\{-x\\in\nN_0({{\\omega}})\\}}{{\\mathbbm{1}}}_{{{\\Omega}}_0}\\right)\\circ{{\\theta}}_x$. This observation implies that $$f\\circ{{\\theta}}_x{{\\mathbbm{1}}}_{{{\\Omega}}_0}{{\\mathbbm{1}}}_{\\{x\\in\nN_0({{\\omega}})\\}}=\\left(f{{\\mathbbm{1}}}_{{{\\Omega}}_0}{{\\mathbbm{1}}}_{\\{-x\\in\nN_0({{\\omega}})\\}}\\right)\\circ{{\\theta}}_x, \\label{lem_chain_environments3}$$ and (\\[lem\\_chain\\_environments2\\]) follows from (\\[lem\\_chain\\_environments3\\]) by the shift invariance of $Q$. From (\\[lem\\_chain\\_environments\\]) we deduce that for any bounded measurable functions $f,g:{{\\Omega}}\\rightarrow{{\\mathbb{R}}}$,\n\n$${{\\mathbb{E}}}_P[f\\cdot (\\Lambda g)]={{\\mathbb{E}}}_P[g\\cdot (\\Lambda f)],\n\\label{inner_product_property}$$\n\nwhere $\\Lambda f:{{\\Omega}}_0\\rightarrow{{\\mathbb{R}}}$ is the function $$(\\Lambda f)({{\\omega}})=\\frac{1}{2d}\\sum_{x\\in{{\\mathbb{Z}}}^d}{\\left({{\\mathbbm{1}}}_{\\{x\\in\nN_0({{\\omega}})\\}}f({{\\theta}}_x{{\\omega}})\\right)}. ", "\\label{Lambda_function}$$ Indeed $${{\\mathbb{E}}}_P[f\\cdot (\\Lambda g)]=\\frac{1}{2d}\\sum_{x\\in{{\\mathbb{Z}}}^d}{{\\mathbb{E}}}_P[f\\cdot g\\circ{{\\theta}}_x{{\\mathbbm{1}}}_{\\{x\\in N_0({{\\omega}})\\}}].$$ Applying (\\[lem\\_chain\\_environments\\]) we get $${{\\mathbb{E}}}_P[f\\cdot (\\Lambda g)]=\\frac{1}{2d}\\sum_{x\\in{{\\mathbb{Z}}}^d}{{\\mathbb{E}}}_P[f\\circ {{\\theta}}_{-x}{{\\mathbbm{1}}}_{\\{-x\\in N_0({{\\omega}})\\}}\\cdot g]={{\\mathbb{E}}}_P[(\\Lambda f)\\cdot g],$$ where we replaced the sign in the sum in order to cancel the negative sign inside the sum. ", "But (\\[inner\\_product\\_property\\]) is the definition of reversibility. ", "Setting $f=1$ and noting that $\\Lambda f=1$, we get that for every bounded measurable function $g:{{\\Omega}}\\rightarrow{{\\mathbb{R}}}$ $${{\\mathbb{E}}}_P[\\Lambda g]={{\\mathbb{E}}}_P[g],$$ and therefore $P$ is stationary with respect to the Markov kernel $\\Lambda$.\n\nThe Kipnis-Varadhan Construction\n--------------------------------\n\n$~$\\\nNext we will adapt the construction of Kipnis and Varadhan [@KV86] cited from [@BB06] to the present analysis. ", "Let $L^2=L^2({{\\Omega}}_0,{{\\mathfrak{B}}},P)$ be the space of all Borel-measurable square integrable functions on ${{\\Omega}}_0$. We will use the notation $L^2$ both for ${{\\mathbb{R}}}$-valued functions as well as for ${{\\mathbb{R}}}^d$-valued functions. ", "We equip $L^2$ with the inner product $(f,g)={{\\mathbb{E}}}_P[fg]$, when for vector valued functions on ${{\\Omega}}$ we interpret $\"fg\"$ as the scalar product of $f$ and $g$. Let $\\Lambda$ be the operator defined by (\\[Lambda\\_function\\]), and we expand the definition to vector valued functions by letting $\\Lambda$ act like a scalar, i.e., independently for each component. ", "From (\\[inner\\_product\\_property\\]) we get that $$(f,\\Lambda g)=(\\Lambda f,g),$$ and so $\\Lambda$ is symmetric. ", "In addition, for every $f\\in L^2$ we have $$|(f,\\Lambda f)|\\leq\\frac{1}{2d}\\sum_{x\\in{{\\mathbb{Z}}}^d}{|(f,{{\\mathbbm{1}}}_{\\{x\\in N_0({{\\omega}})\\}}f\\circ{{\\theta}}_x)|}=\n\\frac{1}{2d}\\sum_{x\\in{{\\mathbb{Z}}}^d}{|(f{{\\mathbbm{1}}}_{\\{x\\in\nN_0({{\\omega}})\\}},{{\\mathbbm{1}}}_{\\{x\\in N_0({{\\omega}})\\}}f\\circ{{\\theta}}_x)|}.$$ Using the Cauchy-Schwartz inequality this is less than or equal to $$\\frac{1}{2d}\\sum_{x\\in{{\\mathbb{Z}}}^d}{(f{{\\mathbbm{1}}}_{\\{x\\in N_0({{\\omega}})\\}},f{{\\mathbbm{1}}}_{\\{x\\in N_0({{\\omega}})\\}})^{1/2}\\cdot({{\\mathbbm{1}}}_{\\{x\\in N_0({{\\omega}})\\}}f\\circ{{\\theta}}_x,{{\\mathbbm{1}}}_{\\{x\\in N_0({{\\omega}})\\}}f\\circ{{\\theta}}_x)^{1/2}},$$ which equals $$\\frac{1}{2d}\\sum_{x\\in{{\\mathbb{Z}}}^d}{(f,f{{\\mathbbm{1}}}_{\\{x\\in N_0({{\\omega}})\\}})^{1/2}\\cdot(1,{{\\mathbbm{1}}}_{\\{x\\in N_0({{\\omega}})\\}}f^2\\circ{{\\theta}}_x)^{1/2}}.$$ Using (\\[lem\\_chain\\_environments\\]) we find that this this equals $$\\frac{1}{2d}\\sum_{x\\in{{\\mathbb{Z}}}^d}{(f,f{{\\mathbbm{1}}}_{\\{x\\in N_0({{\\omega}})\\}})^{1/2}\\cdot(f,f{{\\mathbbm{1}}}_{\\{-x\\in N_0({{\\omega}})\\}})^{1/2}}\\leq\\frac{1}{2d}\\sum_{x\\in{{\\mathbb{Z}}}^d}{(f,f{{\\mathbbm{1}}}_{\\{x\\in N_0({{\\omega}})\\}})}=(f,f),$$ and so $~\\|\\Lambda\\|_{L^2}\\leq 1$. In particular, $\\Lambda$ is self adjoint and $sp(\\Lambda)\\subseteq [-1,1]$.\n\nLet $V:{{\\Omega}}_0\\rightarrow{{\\mathbb{R}}}^d$ be the local drift at the origin i.e, $$V({{\\omega}})=\\frac{1}{2d}\\sum_{x\\in{{\\mathbb{Z}}}^d}{x{{\\mathbbm{1}}}_{\\{x\\in N_0({{\\omega}})\\}}}.", "\n\\label{drift_equation}$$\n\nIf the second moment of $f_e$ exists for every $e\\in{{\\mathcal{E}}}$, then $V\\in L^2$. Indeed $$(V,V)=\\sum_{e\\in{{\\mathcal{E}}}}{(V\\cdot e,V\\cdot e)},$$ and $$(V\\cdot e,V\\cdot e)=\\frac{1}{2d}{{\\mathbb{E}}}_P[(V\\cdot e)^2]=\\frac{1}{2d}{{\\mathbb{E}}}_P[(f_e)^2+(f_{-e})^2],$$ which is finite if the second moments exist. ", "For each ${{\\epsilon}}>0$, let $\\psi_{{\\epsilon}}:{{\\Omega}}_0\\rightarrow{{\\mathbb{R}}}^d$ be the solution of $$(1+{{\\epsilon}}-\\Lambda)\\psi_{{\\epsilon}}=V. \\label{defining_psi_ep}$$ This is well defined since $sp(\\Lambda)\\subset[-1,1]$, so for every ${{\\epsilon}}>0$ we get $sp(1+{{\\epsilon}}+\\Lambda)\\subset[{{\\epsilon}},2+{{\\epsilon}}]$. In addition we get that $\\psi_{{\\epsilon}}\\in L^2$ for all ${{\\epsilon}}>0$. The following theorem is the main result concerning the corrector:\n\nThere is a function $\\chi:{{\\mathbb{Z}}}^d\\times{{\\Omega}}_0\\rightarrow{{\\mathbb{R}}}^d$ such that for every $x\\in{{\\mathbb{Z}}}^d$, $$\\lim_{{{\\epsilon}}\\searrow\n0}{{{\\mathbbm{1}}}_{\\{x\\in{{\\mathcal{P}}}({{\\omega}})\\}}(\\psi_{{\\epsilon}}\\circ{{\\theta}}_x-\\psi_{{\\epsilon}})}=\\chi(x,\\cdot),~~~~~in~\nL^2.$$ Moreover, the following properties hold:\n\n1. ", " (Shift invariance) For $P$-almost every ${{\\omega}}\\in{{\\Omega}}_0$ $$\\chi(x,{{\\omega}})-\\chi(y,{{\\omega}})=\\chi(x-y,{{\\theta}}_y({{\\omega}})),\n \\label{shift_invariance}$$ for all $x,y\\in{{\\mathcal{P}}}({{\\omega}})$.\n\n2. ", " (Harmonicity) For $P$-almost every ${{\\omega}}\\in{{\\Omega}}_0$, the function $$x\\mapsto\\chi(x,{{\\omega}})+x,$$ is harmonic with respect to the transition probability given in (\\[transition\\_probability\\])\n\n3. ", " (Square integrability) There exists a constant $C<\\infty$ such that $$\\|[\\chi(x+y,\\cdot)-\\chi(x,\\cdot)]{{\\mathbbm{1}}}_{\\{x\\in{{\\mathcal{P}}}({{\\omega}})\\}}({{\\mathbbm{1}}}_{\\{y\\in\n N_0({{\\omega}})\\}}\\circ{{\\theta}}_x)\\|_2<C, \\label{square_integrability}$$ for all $x,y\\in{{\\mathbb{Z}}}^d$.\n\n\\[corrector\\_thm\\]\n\nThe rest of this section deals with proving Theorem \\[corrector\\_thm\\]. ", "The proof is based on spectral calculus and closely follows the corresponding arguments from [@BB06] and [@KV86].", "\n\nSpectral calculation\n--------------------\n\n$~$\\\nLet $\\mu_{\\Lambda,V}=\\mu_V$ denote the spectral measure of $\\Lambda:\nL^2\\rightarrow L^2$ associated with the function $V$. i.e, for every bounded, continuous function $\\Phi:[-1,1]\\rightarrow{{\\mathbb{R}}}$, we have $$(V,\\Phi(\\Lambda)V)=\\int_{-1}^{1}{\\Phi(\\lambda)\\mu_V(d\\lambda)}.$$ Since $\\Lambda$ acts as a scalar, $\\mu_V$ is the sum of the “usual” spectral measures for the Cartesian components of $V$. In the integral, we used the fact that $sp(\\Lambda)\\subset[-1,1]$, and therefore the measure $\\mu_V$ is supported entirely on $[-1,1]$. The first observation, made already by Kipnis and Varadhan, is stated as follows:\n\nAssume that the second moments of $\\{f_{\\pm e_i}\\}_{i=1}^{d}$ are finite, then $$\\int_{-1}^{1}{\\frac{1}{1-\\lambda}\\mu_V(d\\lambda)}<\\infty.", "\n\\label{spectral_measure}$$\n\nThe proof follows the proof of Lemma 2.3 in [@BB06]. ", "Let $f\\in\nL^2$ be a bounded real-valued function. ", "Using we get $$\\sum_{x\\in{{\\mathbb{Z}}}^d}{x{{\\mathbb{E}}}_P[f{{\\mathbbm{1}}}_{\\{x\\in\nN_0({{\\omega}})\\}}]}=\\frac{1}{2}\\sum_{x\\in{{\\mathbb{Z}}}^d}x{{\\mathbb{E}}}_P[(f-f\\circ{{\\theta}}_x){{\\mathbbm{1}}}_{\\{x\\in\nN_0({{\\omega}})\\}}]. ", "\\label{symmetry_for_lem}$$ Hence, for every $a\\in{{\\mathbb{Z}}}^d$ we get $$\\begin{aligned}\n(f,a\\cdot V)& = \\frac{1}{2d}\\sum_{x\\in{{\\mathbb{Z}}}^d}{x\\cdot a}{{\\mathbb{E}}}_P[f{{\\mathbbm{1}}}_{\\{x\\in N_0({{\\omega}})\\}}]\\nonumber\\\\\n& = \\frac{1}{2}\\frac{1}{2d}\\sum_{x\\in{{\\mathbb{Z}}}^d}{x\\cdot a}{{\\mathbb{E}}}_P[(f-f\\circ{{\\theta}}_x){{\\mathbbm{1}}}_{\\{x\\in N_0({{\\omega}})\\}}]\\nonumber\\\\\n& \\leq \\frac{1}{2}\\left(\\frac{1}{2d}\\sum_{x\\in{{\\mathbb{Z}}}^d}{(x\\cdot a)^2 P(x\\in N_0({{\\omega}}))}\\right)^{1/2} \\nonumber\\\\\n& \\cdot\n\\left(\\frac{1}{2d}\\sum_{x\\in{{\\mathbb{Z}}}^d}{{{\\mathbb{E}}}_P[(f-f\\circ{{\\theta}}_x)^2{{\\mathbbm{1}}}_{\\{x\\in\nN_0({{\\omega}})\\}}]}\\right)^{1/2}, \\nonumber\n\\end{aligned}$$ where we used in the second equality, and the Cauchy-Schwartz inequality for the inequality. ", "Using the assumption that the second moments of $f_e$ exist for every $e\\in{{\\mathcal{E}}}$, the first term on the right hand side is less than a finite constant times $|a|$. On the other hand, the second term, using , can be written as follows: $$\\begin{aligned}\n\\frac{1}{2d}\\sum_{x\\in{{\\mathbb{Z}}}^d}{{{\\mathbb{E}}}_P((f-f\\circ{{\\theta}}_x)^2{{\\mathbbm{1}}}_{\\{x\\in\nN_0({{\\omega}})\\}})}&\\\\\n&=2\\frac{1}{2d}\\sum_{x\\in{{\\mathbb{Z}}}^d}{{{\\mathbb{E}}}_P(f(f-f\\circ{{\\theta}}_x){{\\mathbbm{1}}}_{\\{x\\in\nN_0({{\\omega}})\\}})} \\nonumber\\\\\n&= 2(f,(1-\\Lambda)f).\\nonumber\n\\end{aligned}$$ From the assumption that the second moments exist, there exists a constant $C_0<\\infty$ such that for all bounded $f\\in L^2$, $$|(f,a\\cdot V)|\\leq C_0|a|\\left(f,(1-\\Lambda)f\\right)^{1/2}.", "\n\\label{bound_for_(f,aV)}$$ Applying for $f$ of the form $f=a\\cdot\\psi(\\Lambda)V$, where $a\\in{{\\mathbb{R}}}^d$, and $\\Psi:[-1,1]\\rightarrow{{\\mathbb{R}}}$ is a bounded continuous function, summing over coordinate vectors in ${{\\mathbb{R}}}^d$ and invoking , we get that $$\\begin{aligned}\n\\left|\\int_{-1}^{1}{\\psi(\\lambda)\\mu_V(d\\lambda)}\\right|\n&= \\left|\\sum_{i=1}^{d}{(V\\cdot e_i,\\psi(\\Lambda)V\\cdot e_i)}\\right| \\nonumber\\\\\n&\\leq \\sum_{i=1}^{d}{\\big|(V\\cdot e_i,\\psi(\\Lambda)V\\cdot e_i)\\big|} \\nonumber\\\\\n&\\leq C_0\\sum_{i=1}^{d}{\\big(V\\cdot e_i,\\psi(\\Lambda)^2(1-\\Lambda)V\\cdot e_i\\big)^{1/2}} \\nonumber\\\\\n&\\leq C_0\\sqrt{d}\\left(\\sum_{i=1}^{d}{\\big(V\\cdot e_i,\\psi(\\Lambda)^2(1-\\Lambda)V\\cdot e_i\\big)}\\right)^{1/2} \\nonumber\\\\\n&=\nC_0\\sqrt{d}\\left(\\int_{-1}^{1}{\\psi(\\lambda)^2(1-\\lambda)\\mu_V(d\\lambda)}\\right)^{1/2}.", "\n\\nonumber\n\\end{aligned}$$ Substituting $\\psi_{{\\epsilon}}(\\lambda)=\\min{\\{\\frac{1}{{{\\epsilon}}},\\frac{1}{1-\\lambda}\\}}$ for $\\psi$ and noting that $(1-\\lambda)\\psi_{{\\epsilon}}(\\lambda)\\leq 1$, we get $$\\int_{-1}^{1}{\\psi_{{\\epsilon}}(\\lambda)\\mu_V(d\\lambda)}\\leq\nC_0\\sqrt{d}\\left(\\int_{-1}^{1}{\\psi_{{\\epsilon}}(\\lambda)\\mu_V(d\\lambda)}\\right)^{1/2},$$ and therefore $$\\int_{-1}^{1}{\\psi_{{\\epsilon}}(\\lambda)\\mu_V(d\\lambda)}\\leq d\\cdot C_0^2.$$ Now, the Monotone Convergence Theorem implies that $$\\int_{-1}^{1}{\\frac{1}{1-\\lambda}\\mu_V(d\\lambda)}=\\lim_{{{\\epsilon}}\\searrow\n0}{\\int_{-1}^{1}{\\psi_{{\\epsilon}}(\\lambda)\\mu_V(d\\lambda)}}=\\sup_{{{\\epsilon}}>0}{\\int_{-1}^{1}{\\psi_{{\\epsilon}}(\\lambda)\\mu_V(d\\lambda)}}\\leq\nd\\cdot C_0^2<\\infty,$$ proving the desired claim.", "\n\nWe now turn to prove the following lemma, also taken from [@BB06]:\n\nLet $\\psi_{{\\epsilon}}$ be defined as in , i.e, the solution of $(1+{{\\epsilon}}-\\Lambda)\\psi_{{\\epsilon}}=V$. Then $$\\lim_{{{\\epsilon}}\\searrow 0}{{{\\epsilon}}\\|\\psi_{{\\epsilon}}\\|_2^2}=0.", "\n\\label{psi_squared_limit}$$ In addition, for every $x\\in{{\\mathbb{Z}}}^d$ let $$G_x^{({{\\epsilon}})}({{\\omega}})={{\\mathbbm{1}}}_{{{\\Omega}}_0}({{\\omega}})\\cdot{{\\mathbbm{1}}}_{\\{x\\in\nN_0({{\\omega}})\\}}({{\\omega}})\\cdot (\\psi_{{\\epsilon}}\\circ{{\\theta}}_x({{\\omega}})-\\psi_{{\\epsilon}}({{\\omega}})).", "\n\\label{G_definition}$$ Then for all $x,y\\in {{\\mathbb{Z}}}^d$, $$\\lim_{{{\\epsilon}}_1,{{\\epsilon}}_2\\searrow\n0}{\\|G_x^{({{\\epsilon}}_1)}\\circ{{\\theta}}_y-G_x^{({{\\epsilon}}_2)}\\circ{{\\theta}}_y\\|_2}=0.", "\n\\label{lim_of_G_exist}$$\n\nThe proof follows the proof in [@BB06]. ", "From the definition of $\\psi_{{\\epsilon}}$ we have, $${{\\epsilon}}\\|\\psi_{{\\epsilon}}\\|_2^2=\\int_{-1}^{1}{\\frac{{{\\epsilon}}}{(1+{{\\epsilon}}-\\lambda)^2}\\mu_V(d\\lambda)}.$$ The integrand is dominated by $\\frac{1}{1-\\lambda}$ and in addition tends to zero as ${{\\epsilon}}\\searrow 0$ in the support of $\\mu_V$. Then follows by the Dominated Convergence Theorem. ", "The second part of the claim is proved similarly: First we get rid of the $y$-dependence by noting the following. ", "Due to the fact that $G_x^{{{\\epsilon}}}\\circ{{\\theta}}^y\\neq 0$ ensure that $y\\in{{\\mathcal{P}}}({{\\omega}})$, and since $P$ is invariant under translation of the form ${{\\theta}}^z~~z\\in{{\\mathcal{P}}}({{\\omega}})$ we get that: $$\\|G_x^{({{\\epsilon}}_1)}\\circ{{\\theta}}_y-G_x^{({{\\epsilon}}_2)}\\circ{{\\theta}}_y\\|_2=\\|G_x^{({{\\epsilon}}_1)}-G_x^{({{\\epsilon}}_2)}\\|_2.", "\n\\label{norm_equality_G}$$ Therefore, averaging the square of over $x\\in N_0({{\\omega}})$ we find that $$\\begin{aligned}\n\\frac{1}{2d}\\sum_{x\\in\nN_0({{\\omega}})}{\\|G_x^{({{\\epsilon}}_1)}\\circ{{\\theta}}_y-G_x^{({{\\epsilon}}_2)}\\circ{{\\theta}}_y\\|_2^2}\n& = \\frac{1}{2d}\\sum_{x\\in N_0({{\\omega}})}{\\|G_x^{({{\\epsilon}}_1)}-G_x^{({{\\epsilon}}_2)}\\|_2^2}\\nonumber\\\\\n&=\\frac{1}{2d}\\sum_{x\\in\nN_0({{\\omega}})}{{{\\mathbb{E}}}_P\\Big[(G_x^{({{\\epsilon}}_1)}-G_x^{({{\\epsilon}}_2)})^2\\Big]} \\\\\n&= \\frac{1}{2d}\\sum_{x\\in {{\\mathbb{Z}}}^d}{{{\\mathbb{E}}}_P\\Big[{{\\mathbbm{1}}}_{{{\\Omega}}_0}{{\\mathbbm{1}}}_{\\{x\\in\nN_0{({{\\omega}})}\\}}(\\Psi\\circ{{\\theta}}_x-\\Psi)^2\\Big]},\n\\end{aligned}$$ where $\\Psi=\\psi_{{{\\epsilon}}_1}-\\psi_{{{\\epsilon}}_2}$. Expanding the last expression we see that it equals to: $$\\frac{1}{2d}\\sum_{x\\in {{\\mathbb{Z}}}^d}{{{\\mathbb{E}}}_P[{{\\mathbbm{1}}}_{{{\\Omega}}_0}{{\\mathbbm{1}}}_{\\{x\\in\nN_0{({{\\omega}})}\\}}(\\Psi^2\\circ{{\\theta}}_x+\\Psi^2-2\\Psi\\cdot\\Psi\\circ{{\\theta}}_x)]}.$$ Since $P$ is stationary under translation ${{\\theta}}_x$ when $x\\in\nN_0({{\\omega}})$, we get that it can be written as $$2(\\Psi,\\Psi)-2\\left(\\Psi,\\frac{1}{2d}\\sum_{x\\in{{\\mathbb{Z}}}^d}{{{\\mathbb{E}}}_P({{\\mathbbm{1}}}_{{{\\Omega}}_0}{{\\mathbbm{1}}}_{\\{x\\in\nN_0{({{\\omega}})}\\}}\\Psi\\circ{{\\theta}}_x)}\\right)=2(\\Psi,(1-\\Lambda)\\Psi).$$ Finally we evaluate $(\\Psi,(1-\\Lambda)\\Psi)$: $$\\begin{aligned}\n\\left(\\psi_{{{\\epsilon}}_1}-\\psi_{{{\\epsilon}}_2},(1-\\Lambda)(\\psi_{{{\\epsilon}}_1}-\\psi_{{{\\epsilon}}_2})\\right)&\n=\\int_{-1}^{1}{\\left(\\frac{1}{(1+{{\\epsilon}}_1-\\lambda)^2}-\\frac{1}{(1+{{\\epsilon}}_2-\\lambda)^2}\\right)(1-\\lambda)\\mu_v(d\\lambda)}\\nonumber\\\\\n&=\\int_{-1}^{1}{\\frac{({{\\epsilon}}_1-{{\\epsilon}}_2)^2(1-\\lambda)}{(1+{{\\epsilon}}_1-\\lambda)^2(1+{{\\epsilon}}_2-\\lambda)^2}\\mu_V(d\\lambda)}.\\nonumber\n\\end{aligned}$$ The integrand here is again bounded by $\\frac{1}{1-\\lambda}$ for all ${{\\epsilon}}_1,{{\\epsilon}}_2>0$, and it tends to zero as ${{\\epsilon}}_1,{{\\epsilon}}_2\\searrow 0$. The claim now follows by the Dominated Convergence Theorem.\\\n\nNow we are finally ready to prove Theorem \\[corrector\\_thm\\].\\\n\nAgain we closely follow the proof of Theorem 2.2 in [@BB06]. ", "Let $G^{{{\\epsilon}}}_x\\circ{{\\theta}}_y$ be as in . ", "Using we know that $G^{{{\\epsilon}}}_x\\circ{{\\theta}}_y$ converges in $L^2$ as ${{\\epsilon}}\\searrow 0$. We denote the limit by $G_{y,y+x}=\\lim_{{{\\epsilon}}\\searrow 0}{G_x^{{\\epsilon}}\\circ{{\\theta}}_y}$. Since $G^{{{\\epsilon}}}_x\\circ{{\\theta}}_y$ is a gradient field on ${{\\mathcal{P}}}({{\\omega}})$, we have $G_{y,y+x}({{\\omega}})+G_{y+x,y}({{\\omega}})=0$ and, more generally $\\sum_{k=0}^{n-1}{G_{x_k,x_{k+1}}}=0$ whenever $(x_0,x_1,\\ldots,x_n)$ is a closed loop on ${{\\mathcal{P}}}({{\\omega}})$. Thus we may define $$\\chi(x,{{\\omega}}):=\\sum_{k=0}^{n-1}{G_{x_k,x_{k+1}}({{\\omega}})},\n\\label{chi_definition}$$ where $(x_0,x_1,\\ldots,x_n)$ is a “nearest neighbor” (in the sense of $x_i\\in N_{x_{i-1}}({{\\omega}})$) path on ${{\\mathcal{P}}}({{\\omega}})$ connecting $x_0=0$ to $x_n=x$. By the above “loop” conditions, the definition is independent of this path for almost every ${{\\omega}}\\in{{\\Omega}}_0\\cap\\{{{\\omega}}:x\\in{{\\mathcal{P}}}({{\\omega}})\\}$. The shift invariance will now follow from the definition of $\\chi$ and the fact that $G_{x,x+y}=G_{0,y}\\circ{{\\theta}}_x$. In light of the shift invariance, to prove the harmonicity of $x\\mapsto x+\\chi(x,{{\\omega}})$ it is sufficient to show that, almost surely, $$\\frac{1}{2d}\\sum_{x\\in\nN_0({{\\omega}})}{\\left[x+\\chi(x,\\cdot)\\right]=\\chi(0,\\cdot)},$$ which can be written as: $$\\frac{1}{2d}\\sum_{x\\in\nN_0({{\\omega}})}{\\left[\\chi(0,\\cdot)-\\chi(x,\\cdot)\\right]}=V({{\\omega}}).$$ By the definition of $\\chi$ we have for $x\\in N_0({{\\omega}})$ that $\\chi(x,\\cdot)-\\chi(0,\\cdot)=G_{0,x}$, therefore the left hand side is the ${{\\epsilon}}\\searrow 0$ limit of $$-\\frac{1}{2d}\\sum_{x\\in{{\\mathbb{Z}}}^d}{G_x^{{\\epsilon}}}=\\frac{1}{2d}\\sum_{x\\in{{\\mathbb{Z}}}^D}{{{\\mathbbm{1}}}_{{{\\Omega}}_0}{{\\mathbbm{1}}}_{\\{x\\in\nN_0({{\\omega}})\\}}(\\psi_e-\\psi_{{\\epsilon}}\\circ{{\\theta}}_x)}=(1-\\Lambda)\\psi_{{\\epsilon}}.$$ Using the definition of $\\psi_{{\\epsilon}}$ , we get that $(1-\\Lambda)\\psi_{{\\epsilon}}=V-{{\\epsilon}}\\psi_{{\\epsilon}}$. From here, using , we get that the ${{\\epsilon}}\\searrow 0$ limit is indeed V in $L^2$.\n\nFinally, we need to show the square integrability . ", "We note that, by the construction of the corrector, $$\\left[\\chi(x+y,\\cdot)-\\chi(x,\\cdot)\\right]{{\\mathbbm{1}}}_{\\{x\\in{{\\mathcal{P}}}({{\\omega}})\\}}{{\\mathbbm{1}}}_{\\{y\\in\nN_0({{\\omega}})\\}}\\circ{{\\theta}}_x=G_{x,x+y}.$$ But $G_{x,x+y}$ is the $L^2$ limit of $L^2$-functions $G_y^{({{\\epsilon}})}\\circ{{\\theta}}_x$ whose $L^2$ norm is bounded by that of $G_y^{{{\\epsilon}}}$. Hence follows with $C=\\max_{\\{x:x\\in N_0{{{\\omega}}}\\}}{\\|G_{0,x}\\|_2}$.\n\nSublinearity along coordinate directions\n========================================\n\nWe are now ready to start treating the main difficulty of the high dimensional Central limit theorem proof: the sublinearity of the corrector. ", "In this section, we treat the sublinearity along the coordinate directions in ${{\\mathbb{Z}}}^d$. Fix $e\\in{{\\mathcal{E}}}$. We define a sequence $n^e_k({{\\omega}})$ inductively by $n^e_1({{\\omega}})=f_e({{\\omega}})$ and $n^e_{k+1}=n^e_k({{\\sigma}}_e({{\\omega}}))$ where ${{\\sigma}}_e$ is the induced translation defined by ${{\\sigma}}_e={{\\theta}}^{f_e({{\\omega}})}_e$. The numbers $n^e_k$ are well-defined and finite almost surely. ", "Let $\\chi$ be the corrector defined in Theorem \\[corrector\\_thm\\]. ", "The main goal of this section is to prove the following theorem:\n\nFor $P$-almost all ${{\\omega}}\\in{{\\Omega}}_0$ $$\\lim_{k\\rightarrow\\infty}{\\frac{\\chi(n^e_k({{\\omega}})e,{{\\omega}})}{k}}=0.$$ \\[coordinate\\_sublinearity\\]\n\nThe proof of this theorem is based on the following properties of $\\chi(n^e_k({{\\omega}})e,{{\\omega}})$:\n\n \\\n\n1. ", " ${{\\mathbb{E}}}_P\\big[|\\chi(n^e_1({{\\omega}})e,\\cdot)|\\big]<\\infty.$\n\n2. ", " ${{\\mathbb{E}}}_P\\big[\\chi(n^e_1({{\\omega}})e,\\cdot)\\big]=0.$\n\n\\[chi\\_moment\\_prop\\]\n\nUsing the definition of the corrector , it follows that $$\\chi(n^e_1({{\\omega}})e,{{\\omega}})=G_{0,n^e_1({{\\omega}})e}({{\\omega}}).$$ By , and since $G_{0,n^e_1({{\\omega}})e}({{\\omega}})$ is the ${{\\epsilon}}\\searrow 0$ limit of $G^{({{\\epsilon}})}_{n^e_1({{\\omega}})e}$ in $L^2$, it follows that $G_{0,n^e_1({{\\omega}})e}({{\\omega}})\\in L^2$. Since $P$ is a probability measure, it is in particular a finite measure, and therefore for every $1\\leq r<2$ it is also true that $G_{0,n^e_1({{\\omega}})e}({{\\omega}})\\in L^r$. Taking $r=1$ we find: $${{\\mathbb{E}}}_P\\big[|\\chi(n^e_1({{\\omega}})e,\\cdot)|\\big]={{\\mathbb{E}}}_P\\big[|G_{0,n^e_1({{\\omega}})e}({{\\omega}})|\\big]<\\infty.$$\n\nIn order to prove part (2), we again use the fact that $G_{0,n^e_1({{\\omega}})e}({{\\omega}})$ is the ${{\\epsilon}}\\searrow 0$ limit in $L^2$ of $G^{({{\\epsilon}})}_{n^e_1({{\\omega}})e}$, and therefore it’s enough to show that for every ${{\\epsilon}}>0$ $${{\\mathbb{E}}}_P\\big[G^{({{\\epsilon}})}_{n^e_1({{\\omega}})e}\\big]=0.$$ and indeed $$\\begin{aligned}\n{{\\mathbb{E}}}_P\\big[G^{({{\\epsilon}})}_{n^e_1({{\\omega}})e}\\big]&={{\\mathbb{E}}}_P\\big[{{\\mathbbm{1}}}_{{{\\Omega}}_0}{{\\mathbbm{1}}}_{\\{n^e_1({{\\omega}})e\\in\nN_0({{\\omega}})\\}}(\\psi_{{\\epsilon}}\\circ{{\\theta}}^{n^e_1({{\\omega}})}_e-\\psi_{{\\epsilon}})\\big]\\nonumber\\\\\n&={{\\mathbb{E}}}_P\\big[{{\\mathbbm{1}}}_{{{\\Omega}}_0}{{\\mathbbm{1}}}_{\\{n^e_1({{\\omega}})e\\in\nN_0({{\\omega}})\\}}\\psi_{{\\epsilon}}\\circ{{\\theta}}^{n^e_1({{\\omega}})}_e\\big]-{{\\mathbb{E}}}_P\\big[{{\\mathbbm{1}}}_{{{\\Omega}}_0}{{\\mathbbm{1}}}_{\\{n^e_1({{\\omega}})e\\in\nN_0({{\\omega}})\\}}\\psi_{{\\epsilon}}\\big]\\nonumber\\\\\n&={{\\mathbb{E}}}_P\\big[({{\\mathbbm{1}}}_{{{\\Omega}}_0}{{\\mathbbm{1}}}_{\\{n^e_1({{\\omega}})e\\in\nN_0({{\\omega}})\\}}\\psi_{{\\epsilon}})\\circ{{\\sigma}}_e\\big]-{{\\mathbb{E}}}_P\\big[{{\\mathbbm{1}}}_{{{\\Omega}}_0}{{\\mathbbm{1}}}_{\\{n^e_1({{\\omega}})e\\in\nN_0({{\\omega}})\\}}\\psi_{{\\epsilon}}\\big],\n\\end{aligned}$$ which equals zero by Theorem \\[induced\\_shift\\_ergodicy\\] and the fact that $\\psi_{{\\epsilon}}$ is absolutely integrable since it is in $L^2$.\n\nLet $g:{{\\Omega}}\\rightarrow{{\\mathbb{R}}}^d$ be defined by $g({{\\omega}})=\\chi(n^e_1({{\\omega}})e,{{\\omega}})$, and let ${{\\sigma}}_e$ be the induced shift in direction e. Then $$\\chi(n^e_k({{\\omega}})e,{{\\omega}})=\\sum_{i=0}^{k-1}{g\\circ{{\\sigma}}_e^i({{\\omega}})}.$$ Using Proposition \\[chi\\_moment\\_prop\\] we have that $g\\in L^1$ and ${{\\mathbb{E}}}_P[g]=0$. Since Theorem \\[induced\\_shift\\_ergodicy\\] ensures ${{\\sigma}}_e$ is $P$-preserving and ergodic, the claim follows from Birkhoff’s Ergodic Theorem.", "\n\nSublinearity everywhere\n=======================\n\nGiven $K > 0$ and ${{\\epsilon}}> 0$, we say that a site $x\\in{{\\mathbb{Z}}}^d$ is $K,\n{{\\epsilon}}$-good in configuration ${{\\omega}}\\in{{\\Omega}}$ if $x\\in{{\\mathcal{P}}}({{\\omega}})$ and $$|\\chi(y,{{\\omega}})-\\chi(x,{{\\omega}})|<K+{{\\epsilon}}|x-y|,$$ holds for every $y\\in{{\\mathcal{P}}}({{\\omega}})$ of the form $y=le$, where $l\\in{{\\mathbb{Z}}}$ and e is a unit coordinate vector. ", "We will use $\\mathcal{G}_{K,{{\\epsilon}}}=\\mathcal{G}_{K,{{\\epsilon}}}({{\\omega}})$ to denote the set of $K,{{\\epsilon}}$-good sites in configuration ${{\\omega}}$.\n\nFor every ${{\\epsilon}}>0$ and $P$-almost every ${{\\omega}}\\in{{\\Omega}}_0$ $$\\limsup_{n\\rightarrow\\infty}{\\frac{1}{(2n+1)^d}\\sum_{x\\in{{\\mathcal{P}}}({{\\omega}}),~|x|\\leq\nn}{{\\mathbbm{1}}}_{\\{|\\chi(x,{{\\omega}})|\\geq {{\\epsilon}}n\\}}}\\leq {{\\epsilon}}.", "\n\\label{sublinearity_formula}$$ \\[sub\\_linearity\\_everywhere\\]\n\nBefore stating the proof, we give a short introduction of the basic idea. ", "This proof is a light modification of the proof from [@BB06].", "\n\nFix the dimension $d$, and for each $\\nu = 1,2,\\ldots, d$ let $\\Lambda_n^\\nu$ be the $\\nu$-dimensional box $$\\Lambda_n^\\nu=\\{k_1 e_1+\\ldots+k_\\nu e_\\nu:k_i\\in{{\\mathbb{Z}}},|k_i|\\leq\nn,\\forall i=1,2,\\ldots,\\nu\\}.$$ We will run an induction over $\\nu$-dimensional sections of the $d$-dimensional box $\\{x\\in{{\\mathbb{Z}}}^d:|x|\\leq n\\}$. The induction eventually gives Theorem \\[sub\\_linearity\\_everywhere\\] for $\\nu=d$ thus proving it. ", "Since it is not advantageous to assume that $0\\in{{\\mathcal{P}}}({{\\omega}})$, we will carry out the proof for differences of the form $\\chi(x,{{\\omega}})-\\chi(y,{{\\omega}})$ with $x,y\\in{{\\mathcal{P}}}({{\\omega}})$. For each ${{\\omega}}\\in{{\\Omega}}$, we thus consider the (upper) density $${{\\mathcal{Q}}}_\\nu({{\\omega}})=\\lim_{{{\\epsilon}}\\downarrow\n0}{\\lim_{n\\rightarrow\\infty}{\\inf_{y\\in\n{{\\mathcal{P}}}({{\\omega}})\\cap\\Lambda_n^1}{\\frac{1}{|\\Lambda_n^1|}{\\sum_{x\\in{{\\mathcal{P}}}({{\\omega}})\\cap\\Lambda_n^\\nu}{{{\\mathbbm{1}}}_{\\{|\\chi(x,{{\\omega}})-\\chi(y,{{\\omega}})|\\geq\n{{\\epsilon}}n\\}}}}}}}. ", "\\label{Q_nu_definition}$$ Note that the infimum is taken only over sites in the one-dimensional box $\\Lambda_n^1$. Our goal is to show by induction that ${{\\mathcal{Q}}}_\\nu=0$ almost surely for all $\\nu=1,\\ldots,d$. The induction step is given by the following lemma:\n\nLet $1\\leq \\nu < d$. If ${{\\mathcal{Q}}}_\\nu=0$ $P$-almost surely, then also ${{\\mathcal{Q}}}_{\\nu+1}=0$ $P$-almost surely. ", "\\[induction\\_lemma\\]\n\nBefore we start the formal proof, we give the main idea: Suppose that ${{\\mathcal{Q}}}_\\nu=0$ for some $\\nu<d$ $P$-almost surely. ", "Pick ${{\\epsilon}}>0$. Then for $P$-almost every ${{\\omega}}$ and all sufficiently large $n$, there exists a set of sites $\\Delta\\subset\\Lambda_n^\\nu\\cap{{\\mathcal{P}}}({{\\omega}})$ such that $$|(\\Lambda_n^\\nu\\cap{{\\mathcal{P}}}({{\\omega}}))\\backslash\\Delta|\\leq\n{{\\epsilon}}|\\Lambda_n^\\nu|, \\label{Lambda_1+property}$$ and $$|\\chi(x,{{\\omega}})-\\chi(y,{{\\omega}})|\\leq{{\\epsilon}}n~~~~\\forall ~x,y\\in\\Delta.", "\n\\label{induction_hypothesis}$$ Moreover, for $n$ sufficiently large, $\\Delta$ could be picked so that $\\Delta\\cap\\Lambda_n^1\\neq\\emptyset$ and, assuming $K\\gg 1$ the non-$K,{{\\epsilon}}$-good sites could be pitched out with little loss of density to achieve even $$\\Delta\\subset \\mathcal{G}_{K,{{\\epsilon}}}. ", "\\label{Lambda_3_property}$$\n\n(All these claims are direct consequences of the Pointwise ergodic Theorem and the fact that $P(0\\in\\mathcal{G}_{K,{{\\epsilon}}})$ converges to $P(0\\in {{\\Omega}})$ as $k\\rightarrow\\infty$.)\\\nAs a result of this construction we have $$|\\chi(z,{{\\omega}})-\\chi(x,{{\\omega}})|\\leq K+{{\\epsilon}}n, \\label{bound_sublinearity}$$\n\nfor any $x\\in\\Delta$ and any $z\\in \\Lambda_n^{\\nu+1}\\cap{{\\mathcal{P}}}({{\\omega}})$ of the form $x+je_{\\nu+1}$. Thus, if $r,s\\in{{\\mathcal{P}}}({{\\omega}})\\cap\\Lambda_n^{\\nu+1}$ are of the form, $r=x+je_{\\nu+1}$ and $s=y+ke_{\\nu+1}$, then implies $$\\begin{aligned}\n|\\chi(r,{{\\omega}})-\\chi(s,{{\\omega}})|&\\leq\n|\\chi(r,{{\\omega}})-\\chi(x,{{\\omega}})|+|\\chi(x,{{\\omega}})-\\chi(y,{{\\omega}})|+|\\chi(y,{{\\omega}})-\\chi(s,{{\\omega}})|\\\\\n&\\leq 2K+2{{\\epsilon}}n + |\\chi(x,{{\\omega}})-\\chi(y,{{\\omega}})|.", "\n\\label{rs-inequality}\n\\end{aligned}$$\n\nInvoking the induction hypothesis , the right hand side is less than $2K+3{{\\epsilon}}n$, implying a bound of the type but one dimension higher. ", "Unfortunately, the above is not sufficient to prove for all but a vanishing fraction of sites in $\\Lambda_n^{\\nu+1}$. The reason is that the $r's$ and $s's$ for which holds, need to be of the form $x+je_{\\nu+1}$ for some $x\\in \\Delta\\cap{{\\mathcal{P}}}({{\\omega}})$. But ${{\\mathcal{P}}}({{\\omega}})$ will occupy only about a $P(0\\in{{\\mathcal{P}}}({{\\omega}}))$ fraction of all sites in $\\Lambda_n^\\nu$, and so this argument does not permit to control more than a fraction of about $P(0\\in {{\\mathcal{P}}}({{\\omega}}))$ of $\\Lambda_n^{\\nu+1}\\cap{{\\mathcal{P}}}({{\\omega}})$.\n\nTo fix this problem, we will have to work with a “stack” of translates of $\\Lambda_n^\\nu$ simultaneously. ", "Explicitly, consider the collection of $\\nu$-boxes $$\\Lambda_{n,j}^\\nu={{\\theta}}^j_{e_{\\nu+1}}(\\Lambda_n^\\nu)~~~~j=1,2\\ldots,L.$$ Here $L$ is a deterministic number chosen so that, for a given $\\delta>0$, the set $$\\Delta_0=\\{x\\in\\Lambda_n^\\nu:\\exists\nj\\in\\{0,1,\\ldots,L-1\\},~x+je_{\\nu+1}\\in\\Lambda_{n,j}^\\nu\\cap{{\\mathcal{P}}}({{\\omega}})\\},$$ is so large that for sufficiently large $n$ $$|\\Delta_0|\\geq (1-\\delta)|\\Lambda_n^\\nu|.$$ These choices ensure that $(1-\\delta)$-fraction of $\\Lambda_n^\\nu$ is now “covered” which, by repeating the above argument, gives us control over $\\chi(r,{{\\omega}})$ for nearly the same fraction of all sites $r\\in\n\\Lambda^{\\nu+1}\\cap{{\\mathcal{P}}}({{\\omega}})$.\n\nLet $\\nu<d$ and suppose that $\\mathcal{Q}_\\nu=0$ $P$-almost surely. ", "Fix $\\delta>0$ with $0<\\delta<\\frac{1}{2}P(0\\in{{\\mathcal{P}}}({{\\omega}}))^2$ and let $L$ be as defined above. ", "Choose ${{\\epsilon}}>0$ so that $$L{{\\epsilon}}+\\delta<\\frac{1}{2}P(0\\in{{\\mathcal{P}}}({{\\omega}}))^2.", "\n\\label{delta_epsilon_assumption}$$ For a fixed but large $K$, $P$-almost every ${{\\omega}}$ and $n$ exceeding an ${{\\omega}}$-dependent quantity, for each $j=1,2,\\ldots,L$, we can find $\\Delta_j\\subset \\Lambda_{n,j}^\\nu\\cap{{\\mathcal{P}}}({{\\omega}})$ satisfying the properties (\\[Lambda\\_1+property\\]-\\[Lambda\\_3\\_property\\]) - with $\\Lambda_n^\\nu$ replaced by $\\Lambda_{n,j}^\\nu$. Given $\\Delta_1,\\ldots,\\Delta_L$, let $\\Lambda$ be the set of sites in $\\Lambda_n^{\\nu+1}\\cap{{\\mathcal{P}}}({{\\omega}})$ whose projection onto the linear subspace $\\mathbb{H}=\\{k_1 e_1+\\ldots+k_\\nu e_\\nu:k_i\\in{{\\mathbb{Z}}}\\}$ belongs to the corresponding projection of $\\Delta_1\\cup\\ldots\\cup\\Delta_L$. Note that the $\\Delta_j$ could be chosen so that $\\Lambda\\cap\\Lambda_n^1\\neq\\emptyset$. By their construction, the projections of the $\\Delta_j's$, $j=1,\\ldots,L$ onto $\\mathbb{H}$ “fail to cover” at most $L{{\\epsilon}}|\\Lambda_n^\\nu|$ sites in $\\Delta_0$, and so at most $(\\delta+L{{\\epsilon}})|\\Lambda_n^\\nu|$ sites in $|\\Lambda_n^\\nu|$ are not of the form $x+ie_{\\nu+1}$ for some $x\\in\\bigcup_j{\\Delta_j}$. It follows that $$|(\\Lambda_n^{\\nu+1}\\cap{{\\mathcal{P}}}({{\\omega}}))\\backslash\\Lambda|\\leq(\\delta+L{{\\epsilon}})|\\Lambda_n^{\\nu+1}|,\n\\label{set_bound}$$ i.e, $\\Lambda$ contains all except at most $(\\delta+L{{\\epsilon}})$-fraction of all sites in $\\Lambda_n^{\\nu+1}$ that we care about. ", "Next we note that if $K$ is sufficiently large, then for every $1\\leq i<j\\leq\nL$, the set $\\mathbb{H}$ contains $\\frac{1}{2}P(0\\in{{\\mathcal{P}}}({{\\omega}}))$-fraction of sites such that $$z_i\\overset{def}{=}x+ie_\\nu\\in\\mathcal{G}_{K,{{\\epsilon}}},~~~~~~z_j=x_je_\\nu\\in\\mathcal{G}_{K,{{\\epsilon}}}.$$ Since we assumed , once $n\\gg 1$, for each pair $(i,j)$ with $1\\leq i<j\\leq L$ such $z_i$ and $z_j$ can be found so that $z_i\\in\\Delta_i$ and $z_j\\in\\Delta_j$. But the $\\Delta_j's$ were picked to make true and so using these pairs of sites we now show that $$\\begin{aligned}\n|\\chi(y,{{\\omega}})-\\chi(x,{{\\omega}})|&\\leq\n|\\chi(y,{{\\omega}})-\\chi(z_j,{{\\omega}})|+|\\chi(z_j,{{\\omega}})-\\chi(z_i,{{\\omega}})|+|\\chi(z_i,{{\\omega}})-\\chi(x,{{\\omega}})|\\\\\n&\\leq {{\\epsilon}}n + K + {{\\epsilon}}L + {{\\epsilon}}n = K+{{\\epsilon}}L+2{{\\epsilon}}n,\n\\label{induction_inequality}\n\\end{aligned}$$ for every $x,y\\in\\Delta_1\\cup\\ldots\\cup\\Delta_L$. From and , we now conclude that for all $r,s\\in\\Lambda$, $$|\\chi(r,{{\\omega}})-\\chi(s,{{\\omega}})|\\leq 3K+{{\\epsilon}}L + 4{{\\epsilon}}n< 5{{\\epsilon}}n,\n\\label{chi_bound}$$ assuming that $n$ is so large that ${{\\epsilon}}n>3K+{{\\epsilon}}L$. If ${{\\mathcal{Q}}}_{\\nu,{{\\epsilon}}}$ denotes the right-hand side of before taking ${{\\epsilon}}\\searrow 0$, the bounds and and the fact that $\\Lambda\\cap \\Lambda_n^1\\neq\\emptyset$ yield $${{\\mathcal{Q}}}_{\\nu+1,5{{\\epsilon}}}({{\\omega}})\\leq \\delta+L{{\\epsilon}},$$ for $P$-almost every ${{\\omega}}$, But the left-hand side of this inequality increases as ${{\\epsilon}}\\searrow 0$ while the right hand side decreases. ", "Thus, taking ${{\\epsilon}}\\searrow 0$ and $\\delta\\searrow 0$ proves that ${{\\mathcal{Q}}}_{\\nu+1}=0$ holds $P$-almost surely.", "\n\nThe proof is an easy consequence of Lemma \\[induction\\_lemma\\]. ", "First, by Theorem \\[coordinate\\_sublinearity\\] we know that ${{\\mathcal{Q}}}({{\\omega}})=0$ for $P$-almost every ${{\\omega}}$. Invoking appropriate shifts, the same conclusion applies $Q$ almost surely. ", "Using induction on dimension, Lemma \\[induction\\_lemma\\] then tells us that ${{\\mathcal{Q}}}_d({{\\omega}})=0$ for $P$ almost every ${{\\omega}}$. Let ${{\\omega}}\\in{{\\Omega}}_0$. By Theorem \\[coordinate\\_sublinearity\\], for each ${{\\epsilon}}>0$ there is $n_0=n_0({{\\omega}})$ with $P(n_0<\\infty)=1$ such that for all $n\\geq\nn_0({{\\omega}})$, we have $|\\chi(x,{{\\omega}})|\\leq {{\\epsilon}}n$ for all $x\\in\n\\Lambda_n^1\\cap {{\\mathcal{P}}}({{\\omega}})$. Using this to estimate away the infimum in , the fact that ${{\\mathcal{Q}}}_d=0$ now immediately implies for all ${{\\epsilon}}>0$.\n\nHigh dimensional Central Limit Theorem\n======================================\n\nThe theorem we wish to prove in this section is the following:\n\nFix $d\\geq 2$. Assume the additional assumption, assumption \\[assumption3\\], then for $P$ almost every ${{\\omega}}\\in{{\\Omega}}_0$ $$\\lim_{n\\rightarrow\\infty}{\\frac{X_n}{\\sqrt{n}}}\\overset{D}{=}N(0,D),$$ where $N(0,D)$ is a $d$-dimensional multivariate normal distribution with covariance matrix $D$ that depends only on $d$ and the distribution of $P$.\n\nWe start with the following lemma:\n\nFix ${{\\omega}}\\in{{\\Omega}}_0$ and let $x\\mapsto \\chi(x,{{\\omega}})$ be the corrector as defined in Theorem \\[corrector\\_thm\\]. ", "given a path of a random walk $\\{X_n\\}_{n=0}^{\\infty}$ on ${{\\mathcal{P}}}({{\\omega}})$ with transition probabilities let $$M_n^{({{\\omega}})}=X_n+\\chi(X_n,{{\\omega}}),~~~~\\forall n\\geq 0.", "\n\\label{deformed_random_walk}$$ Then $\\{M_n^{({{\\omega}})}\\}_{n=0}^{\\infty}$ is an $L^2$-martingale for the filtration $\\{{{\\sigma}}(X_0,X_1,\\ldots,X_n)\\}_{n=0}^{\\infty}$. Moreover, conditional on $X_{k_0}=x$, the increments $\\{M_{k+k_0}^{({{\\omega}})}-M_{k_0}^{({{\\omega}})}\\}_{k=0}^{\\infty}$ have the same law as $\\{M_k^{({{\\theta}}_x{{\\omega}})}\\}_{k=0}^{\\infty}$.\n\nSince $X_n$ is bounded, $\\chi(X_n,{{\\omega}})$ is bounded and so $M_n^{({{\\omega}})}$ is square integrable with respect to $P_{{\\omega}}$. Since $x\\mapsto x+\\chi(x,{{\\omega}})$ is harmonic with respect to the transition probabilities of the random walk $(X_n)$ with law $P_{{\\omega}}$ we have $$E_{{\\omega}}[M_{n+1}^{({{\\omega}})}|{{\\sigma}}(X_n)]=M_n^{({{\\omega}})}~~~\\forall n\\geq 0, P_{{\\omega}}a.s.$$ Since $M_n^{({{\\omega}})}$ is ${{\\sigma}}(X_n)$-measurable, $(M_n^{({{\\omega}})})$ is a martingale. ", "The stated relation between the laws of $(M_{k+k_0}^{({{\\omega}})}-M_{k_0}^{({{\\omega}})})_{k\\geq 0}$ and $(M_k^{({{\\theta}}_x {{\\omega}})})_{k\\geq 0}$ is implied by the shift invariance proved in Theorem \\[shift\\_invariance\\] and the fact that $(M_n^{({{\\omega}})})$ is a simple random walk on the deformed graph.", "\n\nFix $d\\geq 2$, and assume in addition, assumption \\[assumption3\\]. ", "For ${{\\omega}}\\in{{\\Omega}}_0$ let $\\{X_n\\}_{n=0}^\\infty$ be random walk with transition probabilities and let $\\{M_n^{({{\\omega}})}\\}_{n=0}^{\\infty}$ be as defined in . ", "Then for $P$ almost every ${{\\omega}}\\in{{\\Omega}}_0$ we have $$\\lim_{n\\rightarrow\\infty}\\frac{M_n^{({{\\omega}})}}{\\sqrt{n}}\\overset{D}{=}\nN(0,D),$$ where $N(0,D)$ is a $d$-dimensional multivariate normal distribution with covariance matrix $D$ which depends only on $d$ and the distribution $P$, and is given by $D_{i,j}={{\\mathbb{E}}}\\left[cov(M_1^{({{\\omega}})}\\cdot e_i,M_1^{({{\\omega}})}\\cdot\ne_j)\\right]$ \\[Modified\\_CLT\\]\n\nLet $$V_n^{({{\\omega}})}({{\\epsilon}})=\\frac{1}{n}\\sum_{k=0}^{n-1}{E_{{\\omega}}\\left[D_k^{({{\\omega}})}\n{{\\mathbbm{1}}}_{\\{\\min_{i,j}|(D_k^{({{\\omega}})})_{i,j}|\\geq {{\\epsilon}}\\sqrt{n}\n\\}}\\Big|X_0,X_1,\\ldots,X_k\\right]},$$ where $D_k^{({{\\omega}})}$ is the covariance matrix for $M_{k+1}^{({{\\omega}})}-M_k^{({{\\omega}})}$. By the Lindeberg-Feller Central Limit Theorem (see for example [@Du96]), it is enough to show that\\\n\n1. ", " $\\lim_{n\\rightarrow\\infty}{V_n^{({{\\omega}})}(0)}=D$ in $P_{{\\omega}}$-probability.\\\n\n2. ", " $\\lim_{n\\rightarrow\\infty}{V_n^{({{\\omega}})}({{\\epsilon}})}=0$ in $P_{{\\omega}}$-probability for all ${{\\epsilon}}>0$.\\\n\nBoth conditions are implied from Theorem \\[Thm\\_mutual\\_ergodic\\]. ", "Indeed $$V_n^{({{\\omega}})}(0)=\\frac{1}{n}\\sum_{k=0}^{n-1}{h_0\\circ{{\\theta}}_{X_k}({{\\omega}})},\n\\nonumber$$ where $$h_K({{\\omega}})=E_{{\\omega}}\\left[D_1^{({{\\omega}})}\n{{\\mathbbm{1}}}_{\\{\\min_{i,j}|(D_1^{({{\\omega}})})_{i,j}|\\geq K \\}}\\right].$$ Therefore by Theorem \\[Thm\\_mutual\\_ergodic\\] we have for $P$ almost every ${{\\omega}}\\in{{\\Omega}}_0$ $$\\lim_{n\\rightarrow\\infty}{V_n^{({{\\omega}})}(0)}={{\\mathbb{E}}}\\left[h_0({{\\omega}})\\right]=D.$$ On the other hand, for every $K\\in{{\\mathbb{R}}}$ and every ${{\\epsilon}}>0$ we have ${{\\epsilon}}\\sqrt{n}>K$ for sufficiently large $n$, and therefore $f_{{{\\epsilon}}\\sqrt{N}}\\leq f_K$. So $P$-almost surely $$\\limsup_{n\\rightarrow\\infty}{V_n^{({{\\omega}})}({{\\epsilon}})}\\leq\n{{\\mathbb{E}}}\\left[D_1^{({{\\omega}})} {{\\mathbbm{1}}}_{\\{\\min_{i,j}|(D_1^{({{\\omega}})})_{i,j}|\\geq K\n\\}}\\right]\\underset{_{K\\rightarrow\\infty}}{\\longrightarrow}~ 0.$$ Where in order to apply the Dominated Convergence, we used the fact that $M_1^{({{\\omega}})}\\in L^2$.\n\nWe are now ready to prove the high dimensional Central Limit Theorem\n\nDue to Theorem \\[Modified\\_CLT\\] it is enough to prove that for $P$-almost every ${{\\omega}}\\in{{\\Omega}}_0$ $$\\lim_{n\\rightarrow\\infty}{\\frac{\\chi(X_n,{{\\omega}})}{\\sqrt{n}}}=0~~~P_{{\\omega}}~a.s.$$ This will follow if we will show that there exists a constant $K>0$ such that for every ${{\\epsilon}}>0$ and for $P$-almost every ${{\\omega}}\\in{{\\Omega}}_0$ $$\\lim_{n\\rightarrow\\infty}{P_{{\\omega}}\\{|\\chi(X_n,{{\\omega}})|>{{\\epsilon}}\\sqrt{n}\\}}<K{{\\epsilon}}.$$ By Theorem \\[asymptotic\\_X\\_n\\] and the Markov inequality, there exists a random $c=c({{\\omega}}>0$, $P$ almost surely finite, such that that for $P$-almost every ${{\\omega}}\\in{{\\Omega}}_0$ $$P_{{\\omega}}\\left[\\|X_n\\|>\\frac{1}{{{\\epsilon}}}\\sqrt{n}\\right]\\leq\n{{\\epsilon}}\\frac{{{\\mathbb{E}}}_{{\\omega}}(\\|X_n\\|)}{\\sqrt{n}}\\leq c{{\\epsilon}}.\\label{Markov_X_n}$$ We therefore get $$\\begin{aligned}\nP_{{\\omega}}\\left(|\\chi(X_n,{{\\omega}})|>{{\\epsilon}}\\sqrt{n}\\right) \\nonumber\n\\leq P_{{\\omega}}\\left(\\|X_n\\|>\\frac{\\sqrt{n}}{{{\\epsilon}}}\\right)+\nP_{{\\omega}}\\left(\\chi(X_n,{{\\omega}})>{{\\epsilon}}\\sqrt{n},\\|X_n\\|\\leq\\frac{\\sqrt{n}}{{{\\epsilon}}}\\right).\\nonumber\n\\end{aligned}$$ By we find that this is less or equal than $$c{{\\epsilon}}+ \\sum_{x\\in\n{{\\mathcal{P}}}({{\\omega}})}P_{{\\omega}}^n(0,x){{\\mathbbm{1}}}_{\\left\\{|\\chi(x,{{\\omega}})|>{{\\epsilon}}\\sqrt{n},~x\\in\\left[-\\frac{\\sqrt{n}}{{{\\epsilon}}},\\frac{\\sqrt{n}}{{{\\epsilon}}}\\right]\\right\\}}.", "\n\\nonumber$$ Using now Theorem \\[bound\\_of\\_transitions\\] for sufficiently $n$ if follows that $$P_{{\\omega}}\\left(|\\chi(X_n,{{\\omega}})|>{{\\epsilon}}\\sqrt{n}\\right)\\leq c{{\\epsilon}}+\\frac{K_1}{(n-K_2)^\\frac{d}{2}}\\sum_{x\\in {{\\mathcal{P}}}({{\\omega}})\\cap\n\\left[-\\frac{\\sqrt{n}}{{{\\epsilon}}},\\frac{\\sqrt{n}}{{{\\epsilon}}}\\right]}{{{\\mathbbm{1}}}_{\\left\\{\\chi(x,{{\\omega}})>{{\\epsilon}}\\sqrt{n}\\right\\}}}.", "\n\\nonumber$$ Therefore by Theorem \\[sub\\_linearity\\_everywhere\\] we get that there exist constants $c_0,K$ such that $$\\lim_{n\\rightarrow\\infty}{P_{{\\omega}}(|\\chi(X_n,{{\\omega}})|>{{\\epsilon}}\\sqrt{n})}\\leq c{{\\epsilon}}+c_0{{\\epsilon}}^2\\leq K{{\\epsilon}}\\nonumber$$ As required.", "\n\nSome Conjectures And Questions\n==============================\n\nWhile we have full classification of transience recurrence of random walks on discrete point processes in dimensions $d=1$ and $d\\geq 3$, we only have a partial classification in dimension 2. ", "We therefore give the following two conjectures:\n\nThere are transient two dimensional random walks on discrete point processes.", "\n\nThe condition given in Theorem \\[tran\\_recu2\\], for recurrence of 2-dimensional random walk on discrete point process, i.e, the existence of a constant $C>0$ such that $$\\sum_{k=N}^{\\infty}{\\frac{k\\cdot\nP(f_{e_i}=k)}{{{\\mathbb{E}}}(f_{e_i})}}\\leq\\frac{C}{N}~~~i\\in\\{1,2\\}~~N\\in{{\\mathbb{N}}}$$ is not necessary.", "\n\nIn Theorem \\[CLT2\\] we gave conditions for the random walk on discrete point processes to satisfy a Central Limit Theorem. ", "However, we didn’t give any example for a random walk without a Central Limit Theorem. ", "We therefore give the following conjecture:\n\nThere are random walks on discrete point processes in high dimensions that don’t satisfy a Central Limit Theorem.", "\n\nIn the proof of Theorem \\[CLT2\\], we used the additional assumption that there exists ${{\\epsilon}}_0>0$ such that for every coordinate direction $e$ $E_P[f_e^{2+{{\\epsilon}}_0}]<\\infty$. The assumption that the second moments are finite, is fundamental in our proof in order to build the corrector, and seems to be necessary for the CLT to hold. ", "On the other hand, existence of such ${{\\epsilon}}_0>0$ though needed in our proof, was used only in order to bound . ", "We therefore give the following condition:\n\nTheorem \\[CLT2\\] is true even with the weak assumption that only the second moments are finite.", "\n\nEven if the theorem is true with the weak assumption that only the second moment of the distances between points is finite, we can still ask the following question:\n\nIs the condition given in Theorem \\[CLT2\\] also necessary, or can one find examples for random walks on discrete point processes that satisfy a Central Limit Theorem but don’t have all of their second moments finite? ", "We conjecture that such examples exist, but didn’t verified it.", "\n\nWe also have the following conjecture about the Central Limit Theorem:\n\nUnder assumptions \\[Assumptions\\] and \\[assumption3\\], The Central Limit Theorem, \\[CLT2\\], can be strengthened as follows: Random walk on discrete point process under appropriate scaling converges to Brownian motion.", "\n\nOur model describes non nearest neighbors random walk on random subset of ${{\\mathbb{Z}}}^d$ with uniform transition probabilities. ", "We suggest the following generalization of the model:\n\nFix $\\alpha\\in{{\\mathbb{R}}}$. We look on the same model for the environments with transition probabilities as follows: for ${{\\omega}}\\in{{\\Omega}}_0$ $$P_{{\\omega}}(X_{n+1}=u|X_n=v)=\\left\\{\n\\begin{array}{cc}\n0&~~~u\\notin N_v({{\\omega}}) \\\\\n\\frac{1}{Z(v)}\\|u-v\\|^\\alpha&~~~u\\in N_v({{\\omega}})\n\\end{array}\n\\right. ,", "$$ where $Z(v)$ is normalization constant (The case $\\alpha=0$ is the uniform distribution case). ", "What can be proved about the extended model?", "\n\nAppendix {#appendix .unnumbered}\n========\n\nIn this Appendix we prove there exists a constant $c=c(d)>0$ such that for every $0<a\\leq 2$ $$\\sum_{n=0}^{\\infty}e^{-a\\cdot 2^n} \\leq ca^{-d}$$\n\nFirst, we can restrict ourselves to $0<a<{{\\epsilon}}$ for any fixed ${{\\epsilon}}>0$. This follows from the fact that both expressions are monotonic in $a$. Next we note that: $$\\begin{aligned}\n\\sum_{n=0}^{\\infty}{e^{-a\\cdot 2^n}\\cdot 2^{nd}}& \\leq 1+\\sum_{n=1}^\\infty \\frac{1}{1-2^{-d}}\\sum_{k=2^{n-1}d}^{2^n d}e^{-a2^n}\n\\leq \\frac{1}{1-2^{-d}} \\sum_{k=0}^\\infty e^{-ak^{1/d}}\\\\\n&=\\frac{1}{1-2^{-d}} \\sum_{j=0}^\\infty e^{-aj}\\#\\{j<k^{1/d}\\leq j+1\\}\n=\\frac{1}{1-2^{-d}} \\sum_{j=0}^\\infty e^{-aj}[(j+1)^d-j^d].\\nonumber\n\\end{aligned}$$ Since there exists a constant $c=c(d)>0$ such that for every $j\\geq 0$ we have $(j+1)^d-j^d\\leq cj^{d-1}$ the last term is less than or equal to $$\\label{appendix_a1}\n\\frac{c}{1-2^{-d}}\\sum_{j=0}^\\infty e^{-aj}j^{d-1}.$$ For $j\\geq 0$ denote $\\alpha_j=e^{-aj}j^{d-1}$ and define $j_0=\\min\\left\\{j\\geq 0 ~:~ \\forall i\\geq j~~\\frac{a_{i+1}}{a_i}<e^{-a/2}\\right\\}.$ From the definition of $j_0$ it follows that is less than $$\\label{appendix_a2}\n\\begin{aligned}\n\\frac{c}{1-2^{-d}}\\left[\\sum_{j=0}^{j_0-1} a_j+\\sum_{j=j_0}^\\infty a_j \\right]&\\leq \\frac{c}{1-2^{-d}}\\left[\\sum_{j=0}^{j_0-1} a_j+\\sum_{j=j_0}^\\infty a_{j_0}e^{-a(j-j_0)/2} \\right].\\\\\n&\\leq \\frac{c}{1-2^{-d}}\\left[j_0^{d-1}+\\frac{\\alpha_{j_0}}{1-e^{-a/2}}\\right].", "\n\\end{aligned}$$ From the definition of $j_0$ one can see that $j_0=\\left\\lceil\\frac{1}{e^{\\frac{a}{2d}}-1}\\right\\rceil\\leq \\left\\lceil\\frac{2d}{a}\\right\\rceil$, and therefore equals to $$\\frac{c}{1-2^{-d}}\\left(1+\\frac{e^{-a \\left\\lceil\\frac{2d}{a}\\right\\rceil}}{\\frac{a}{2}e^{-a/2}}\\right)\\left\\lceil\\frac{2d}{a}\\right\\rceil^{d-1}$$ which for an appropriate constant $c=c(d)>0$ is less than $ca^{-d}$, as required.", "\n" ]

{ "pile_set_name": "ArXiv" }

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[ "Prostate cancer mediates osteoclastogenesis through two different pathways.", "\nThe present study was undertaken to test the effects of prostate cancer cell lines (LNCaP, DU145, PC3, and MDA PCa 2b) on osteoclastogenesis. ", "Crude conditioned medium (CM) from all four prostate cancer cell lines enhanced expression of the mRNA for receptor activator of NF-kappaB ligand (RANKL) in a mouse osteoblast cell line, MC3T3-E1; however, CM had no effect on expression of osteoprotegerin (OPG) mRNA. ", "Coculture of MC3T3-E1 with prostate cancer cells yielded similar results. ", "The number of mature osteoclasts induced by soluble RANKL increased significantly when osteoclast precursor cells were cultured with CM from LNCaP and DU145 cells. ", "CM from LNCaP and DU145 cells also induced maturation from precursor in the absence of soluble RANKL, and this effect was not blocked by OPG. ", "Addition of CM from DU145 cells increased expression of MMP-9 mRNA by osteoclast precursors. ", "Our findings indicate that prostate cancer mediates osteoclastogenesis through induction of RANKL expression by osteoblasts and through direct actions on osteoclast precursors mediated by some factors other than RANKL." ]

{ "pile_set_name": "PubMed Abstracts" }

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[ "1. ", "Field of the Invention\nThe present invention relates to an image forming apparatus, and more particularly to an image forming apparatus in which an electrostatic latent image is formed on a latent image bearing member such as a photosensitive member with electroconductive toner.", "\n2. ", "Description of the Prior Art\nPopularization of various image forming apparatus such as electrophotographic copiers and electrostatic recorders has induced a danger of illegal copying of private documents which the author does not wish to be copied, or official documents or banknotes.", "\nA conventional countermeasure against such undesired copying consists of using, in the paper of the original document, watermarks or the like which do not appear or appear darker in the copy to facilitate the distinction of the copies from the originals. ", "In such method, however, the paper to be used as the original is of a limited quality and is inevitably expensive. ", "Besides such paper should not be easily available in order to prevent the use of such paper as the copying sheet.", "\nAnother countermeasure consists of marking an identification image in the copy of the original image. ", "Such marking can be achieved by the use of plural exposure systems respectively for the original image and the identification image, or by conducting plural image forming cycles to superpose the identification image with the original image. ", "In such method it is quite easy to form a black identification image in a white area of the copy or to form a white identification image in a black area of the copy. ", "Such method is however not necessarily effective in case the original image does not have a determined pattern, since an identification image of a color which is the same as that of the copied image, or a white identification image on a white area is not easily recognizable." ]

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[ "North Korea has once again threatened to “retaliate against the U.S. with tremendous muscle” if the country does not cancel military exercises with South Korea and other countries, which is scheduled to begin Monday.", "\n\nThe exercises and the threats are nothing new. ", "South Korea conducts the yearly exercises, called Ulchi Freedom Guardian, with the United States and other allies “to enhance… readiness, protect the region and maintain stability on the Korean peninsula,” according to a statement from the Korea-U.S. Combined Forces Command and reported by CNN.", "\n\nNorth Korea creates its own time zone as a snub to “wicked Japanese imperialists” http://t.co/Fz1LZcA232 pic.twitter.com/ZqHteN3nkz — Carbonated.", "TV (@CarbonatedTV) August 7, 2015\n\nJust like the war games are a yearly event, so is North Korea’s threats of retaliation.", "\n\nThis year, a spokesman for North Korea’s National Defense Commission upped the level of threats, as reported by the International Business Times.", "\n\n“The further Ulchi Freedom Guardian joint military exercises are intensified, the strongest military counteraction the (Democratic People’s Republic of Korea) will take to cope with them.”", "\n\nAn official with the State Department told CNN on Saturday that they were aware of the threats and reiterated that the exercises are “transparent, defense-minded and are designed to increase the readiness of South Korea and the region.”", "\n\n“These exercises are a clear demonstration of the U.S. commitment to the alliance.”", "\n\nThe reclusive regime seems to feel a sudden surge of confidence in its military might, according to a NDC spokesman.", "\n\n“The army and people of the DPRK are no longer what they used to be in the past when they had to counter the U.S. nukes with rifles is the invincible power equipped with both [the] latest offensive and defensive means unknown to the world.”", "\n\nN Korea threatens to ‘invade US’ unless S Korean military exercises aren’t halted http://t.co/xUQGDqgfWf pic.twitter.com/F7NPuR53Hq — RT (@RT_com) August 16, 2015\n\nA North Korean state television report went so far as to threaten to attack the U.S. on its own soil.", "\n\n“If [the] United States wants their mainland to be safe, then the Ulchi Freedom Guardian should stop immediately.”", "\n\nA former Army general who participated in previous Ulchi exercises, Lt. ", "Gen. Mark Hurtling, said the regime’s rhetoric is just an attempt to get noticed.", "\n\n“One of the key propaganda goals of the young leader is to just get on the radar of the U.S. With all the other things we’re focused on — ISIS, al Qaida in the Arabian Peninsula, Russia and Ukraine, etc., ", "Kim Jong Un wants to ensure he grabs attention.”", "\n\nDespite North Korea’s threat, the military exercises, which will also include forces from Australia, Canada, Colombia, Denmark, France, New Zealand, and the United Kingdom, is scheduled to begin Monday and will conclude August 28.", "\n\n[Photo by Chung Sung-Jun/Getty Images]" ]

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[ "Effects of adolescence-onset hypogonadism on metabolism, bone mineral density and quality of life in adulthood.", "\nIn a cross-sectional study of 54 patients with adolescence-onset hypogonadism (33 females, 21 males; age range: 19-40 years), medical care, quality of life, and health status were assessed. ", "Most patients had received adequate medical care with short cumulative periods of interruption of hormone replacement. ", "The prevalence of the metabolic syndrome was 27% in females and 19% in males. ", "In comparison to the general population, females had both a lower bone mineral density (dual-energy X-ray absorptiometry, Z-score=-0.8, p<0.001) and a higher prevalence of obesity (age 19-29 years: study population 35%, general population 4%). ", "The body fat percentage (dual-energy X-ray absorptiometry) was significantly elevated (age 19-29 years: females Z-score=+1.8, p<0.001, males Z-score=+2.4, p=0.001). ", "Quality of life (SF-36) was normal. ", "Despite adequate treatment, patients with early-onset hypogonadism are prone to develop signs and symptoms consistent with inadequate hormone replacement. ", "A successful transition from pediatric to adult medicine seems important to optimize treatment outcomes." ]

{ "pile_set_name": "PubMed Abstracts" }

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[ "/*\n * Copyright © 2014 Canonical Ltd.\n *\n * This program is free software: you can redistribute it and/or modify it\n * under the terms of the GNU General Public License version 2 or 3,\n * as published by the Free Software Foundation.", "\n *\n * This program is distributed in the hope that it will be useful,\n * but WITHOUT ANY WARRANTY; without even the implied warranty of\n * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. ", " See the\n * GNU General Public License for more details.", "\n *\n * You should have received a copy of the GNU General Public License\n * along with this program. ", " If not, see <http://www.gnu.org/licenses/>.", "\n *\n * Authored by: Andreas Pokorny <[email protected]>\n */\n\n#include \"../logging_report_factory.h\"\n\n#include \"compositor_report.h\"\n#include \"connector_report.h\"\n#include \"display_report.h\"\n#include \"message_processor_report.h\"\n#include \"scene_report.h\"\n#include \"session_mediator_report.h\"\n#include \"shell_report.h\"\n#include \"input_report.h\"\n#include \"seat_report.h\"\n#include \"mir/logging/shared_library_prober_report.h\"\n\n#include \"mir/default_server_configuration.h\"\n\nnamespace mr = mir::report;\n\nmr::LoggingReportFactory::LoggingReportFactory(std::shared_ptr<mir::logging::Logger> const& logger,\n std::shared_ptr<time::Clock> const& clock)\n : logger(logger),\n clock(clock)\n{\n}\n\nstd::shared_ptr<mir::compositor::CompositorReport> mr::LoggingReportFactory::create_compositor_report()\n{\n return std::make_shared<logging::CompositorReport>(logger, clock);\n}\n\nstd::shared_ptr<mir::graphics::DisplayReport> mr::LoggingReportFactory::create_display_report()\n{\n return std::make_shared<logging::DisplayReport>(logger);\n}\n\nstd::shared_ptr<mir::scene::SceneReport> mr::LoggingReportFactory::create_scene_report()\n{\n return std::make_shared<logging::SceneReport>(logger);\n}\n\nstd::shared_ptr<mir::frontend::ConnectorReport> mr::LoggingReportFactory::create_connector_report()\n{\n return std::make_shared<logging::ConnectorReport>(logger);\n}\n\nstd::shared_ptr<mir::frontend::SessionMediatorObserver> mr::LoggingReportFactory::create_session_mediator_report()\n{\n return std::make_shared<logging::SessionMediatorReport>(logger);\n}\n\nstd::shared_ptr<mir::frontend::MessageProcessorReport> mr::LoggingReportFactory::create_message_processor_report()\n{\n return std::make_shared<logging::MessageProcessorReport>(logger, clock);\n}\n\nstd::shared_ptr<mir::input::InputReport> mr::LoggingReportFactory::create_input_report()\n{\n return std::make_shared<logging::InputReport>(logger);\n}\n\nstd::shared_ptr<mir::input::SeatObserver> mr::LoggingReportFactory::create_seat_report()\n{\n return std::make_shared<logging::SeatReport>(logger);\n}\n\nstd::shared_ptr<mir::SharedLibraryProberReport> mr::LoggingReportFactory::create_shared_library_prober_report()\n{\n return std::make_shared<mir::logging::SharedLibraryProberReport>(logger);\n}\n\nstd::shared_ptr<mir::shell::ShellReport> mir::report::LoggingReportFactory::create_shell_report()\n{\n return std::make_shared<mir::logging::ShellReport>(logger);\n}\n" ]

{ "pile_set_name": "Github" }

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[ "MEDIA ADVISORY — Children’s Rights: Making Canada better for young people with Jean-Yves Duclos, Jim Munson and Irwin Elman\n\nPosted on Monday, November 21, 2016\n\nThe University of Ottawa’s Interdisciplinary Research Laboratory on the Rights of the Child invites members of the media to attend a series of events on children’s rights on Tuesday, November 22, 2016.", "\n\nChildren’s rights: Making Canada work better for young people with Irwin Elman and Senator Jim Munson\n\nWorkshop and speech by the Honourable Jean-Yves Duclos, Minister of Families, Children and Social Development\n\nWHAT: Workshop on how children's rights can improve intergovernmental progress for children in Canada followed by a speech by the Honourable Jean-Yves Duclos, Minister of Families, Children and Social Development\n\nWHEN: Tuesday, November 22, 2016 at 1:15 p.m. (the speech will be delivered at 3:30 p.m. following the workshop)\n\nThe Interdisciplinary Research Laboratory on the Rights of the Child (IRLRC) aims to create a national and international network of researchers and practitioners from various child-related disciplines. ", "Discussion among the many specialists will result in a transfer of knowledge and information, practical on-the-ground benefits, and the development of future joint training and research opportunities between members of academia and front-line workers." ]

{ "pile_set_name": "Pile-CC" }

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[ "Q:\n\nHow do I get (a, b) => c from a => b => c in Scala?", "\n\nIf I have:\nval f : A => B => C\n\nThis is shorthand for:\nval f : Function1[A, Function1[B, C]]\n\nHow do I get a function g with the signature:\nval g : (A, B) => C = error(\"todo\")\n\n(i.e.)\nval g : Function2[A, B, C] //or possibly\nval g : Function1[(A, B), C]\n\nin terms of f?", "\n\nA:\n\nscala> val f : Int => Int => Int = a => b => a + b\nf: (Int) => (Int) => Int = <function1>\n\nscala> Function.uncurried(f)\nres0: (Int, Int) => Int = <function2>\n\nA:\n\nExtending retonym's answer, for completeness\nval f : Int => Int => Int = a => b => a + b\nval g: (Int, Int) => Int = Function.uncurried(f)\nval h: ((Int, Int)) => Int = Function.tupled(g)\n\nThe converse functions for both of these operations are also provided on the Function object, so you could write the above backwards, if you wished\nval h: ((Int, Int)) => Int = x =>(x._1 + x._2)\nval g: (Int, Int) => Int = Function.untupled(h)\nval f : Int => Int => Int = g.curried //Function.curried(g) would also work, but is deprecated. ", "Wierd\n\nA:\n\nJust to round out the answer, although there is a library method to do this, it may also be instructive to do it by hand:\nscala> val f = (i: Int) => ((s: String) => i*s.length)\nf: (Int) => (String) => Int = <function1>\n\nscala> val g = (i: Int, s: String) => f(i)(s)\ng: (Int, String) => Int = <function2>\n\nOr in general,\ndef uncurry[A,B,C](f: A=>B=>C): (A,B)=>C = {\n (a: A, b: B) => f(a)(b)\n}\n\n" ]

{ "pile_set_name": "StackExchange" }

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[ "Author: Petr Kovar\n\nThe GNOME Documentation Team last met for a documentation hackfest back in 2015, following the Open Help Conference hosted by Shaun. ", "After my not so successful attempt at organizing a meetup for both upstream and downstream (Ubuntu) teams to hack on GNOME docs some time in 2017, we finally succeeded in meeting in the upstream format for the West Coast Hackfest from 18th through 21st July 2019. ", "That event organization was kicked off by the folks from the GNOME Engagement team and Foundation staff and gave us an opportunity to hold a co-located event with Documentation, Engagement and the GTK team sharing the venue and allowing for more focused cross-team collaboration.", "\n\nAfter the 3-year long hiatus in having hackfests, the docs team’s primary goal was to get back on track with triaging outstanding documentation bugs for the GNOME documentation core set (GNOME Help and the System Administration Guide). ", "We did not only work on the triaged bugs but made an effort to fix as many parts of the user help as possible, reviewing the content mostly written several years ago against the new features that in the meantime landed in GNOME.", "\n\nThe group that gathered at the hackfest, David, Michael and Jim, are all veteran GNOME writers responsible for authoring a substantial part of the current documentation set, so we didn’t have to spend additional time getting up to speed with the writing process. ", "After the initial doc bug triaging in the gnome-user-docs and gnome-getting-started-docs projects on GitLab, we were off to writing.", "\n\nIn previous sprints, we sometimes struggled with getting an easy-to-use early access to development versions of GNOME that would allow us to quickly focus on the writing. ", "This year we were much better prepared with the availability of Fedora Silverblue. ", "Switching to a rawhide branch from the running system to get the latest bits turned out to be easy, whether we ran the system on bare metal or in a VM, though we also faced some problems often found in development versions, for example, the Wi-Fi adapter on one of the laptops wouldn’t work.", "\n\nWe had a look at making our docs module continuous integration much more robust. ", "We now fail on unsuccessful merge of translated strings when building translations by switching itstool to strict mode:\n\n./autogen.sh ITSTOOL=\"/usr/bin/itstool --strict\"\n\nThis change should make the common problems with missing XML tags in translations more visible.", "\n\nWe now also call yelp-check tests from gitlab-ci.yml as those are not run during make check or distcheck. ", "Last but not least, we run a bunch of xmllint –schematron tests that check for problems such as a missing legal notice include, missing <desc> element, etc. ", "Turned out those tests were written many years ago by Shaun but that somehow slipped through the cracks for the team and the tests would not really be run.", "\n\nAs this hackfest was a co-located event, I also had a chance to sit down with the Engagement team too to go through some of the wiki pages for contributors to both GNOME documentation and localization and identify outdated information or areas for improvement.", "\n\nMost of the core hackfest days were spent on updating different areas of GNOME Help topics, reviewing the content against recent (and not so recent) changes in the UI. ", "However, we also touched on the subject of the future of the GNOME documentation site and using the Pintail site builder we want to deploy as a replacement for the old library-web, which over the years became mostly unmaintained, now missing support for building Mallard documentation from Meson-based tarballs, for example.", "\n\nWith the GNOME initiative from last year attempting to bring up a new site for developer documentation, the project requirements for the developer docs and user and sysadmin docs seem to be slightly different. ", "The developer site hosts, for the larger part, narrative content such as tutorials as well as API reference. ", "It might make sense to treat these two areas separately and and come up with a different approach to each of these, not necessarily using the same build process as it is now.", "\n\nFor the user and sysadmin documentation site, on the other hand, our primary goal is to use a solution that let us keep using the current Mallard-based documentation format and toolchain. ", "Pintail is a tool Shaun wrote for generating the projectmallard.org site that documents the Mallard format itself. ", "It adds all the navigation and translation logic on top of the Mallard-based content, but the most substantial difference from the library-web is that the build process is not based on released tarballs containing documentation, but it simply builds the content from a live git version, working with the git repos and branches directly. ", "That gets the whole build process closer to the popular idea of treating docs as a code and having a continuously updated preview of the docs available on the docs site.", "\n\nWe originally planned to preview a local instance of the Pintail-based help.gnome.org site Shaun prepared a while ago, but then we ran into some build issues that need to be tackled later when we have Shaun around.", "\n\nHaving said that, reworking our docs site remains the very top priority for us, but I’d like our team consider working on other longer-term goals, as well, such as switching to the Ducktype lightweight documentation format, which would get the writing experience much closer to what other popular open source documentation projects out there started to use (Markdown, AsciiDoc, reStructuredText) instead of the once much more popular XML-based formats.", "\n\nIn addition to that, there are more project tasks that we did not have time to focus on this time, with one of them being redesigning the landing page and navigation experience for GNOME Help. ", "That one will need to be given more thought and feedback on how we want to structure the topmost topics and what we want to show the user upon opening Help. ", "A part of that work should be finishing the overhaul of getting started topics and replacing most of the getting started videos with easier-to-maintain SVG graphics.", "\n\nAt the hackfest venue, which turned out to be a really nice co-working space south of Portland downtown, David shot a timelapse video with the team busy at hacking, that I wanted to link from here, too.", "\n\nI’d like to thank the GNOME Foundation for funding my travel, the Foundation staff for helping organize the event, and Red Hat for sponsoring my time at the hackfest.", "\n\nBack from GUADEC, held in the beautiful Andalusian city of Almería, Spain, from 6th July through 11th July, 2018, I wanted to share a few notes wrt documentation and localization activities at the conference and during the traditional post-conference hacking days.", "\n\nMike Hill and Rudolfs Mazurs already blogged about their reflections of GUADEC. ", "I’d add that we had some i18n and L10n-related talks in the schedule (machine translations, input methods), which was a nice improvement in terms of representation from previous years.", "\n\nThe space available for the Birds of a Feather sessions this year was rather limited, so we could only secure an afternoon slot (thanks Kat!) ", "for our docs+translators meetup. ", "We were joined for a while by a group of local documentation writers creating Spanish manuals for the local market. ", "After that, we focused on two main areas.", "\n\nOne was related to the recent migration of GNOME projects to GitLab and involved looking into usability of our wiki docs for contributors and, specifically, newcomers. ", "We found quite a few outdated references to git.gnome.org, Bugzilla and the like, with the biggest issue, however, being the suboptimal overall structure of the contributor guides on the wiki. ", "We also looked into how to improve submitting user feedback and switching languages for the users of help.gnome.org (and yelp).", "\n\nThe other area discussed was making our CI checks for GNOME documentation modules much more robust, with the idea of using the GitLab CI integration to its full potential with tests verifying translations and more.", "\n\nFirst of all, as others have reported, at this year’s GUADEC, it was great to see an actual increase in numbers of attendees compared to previous years. ", "This shows us that 20 years later, the community as a whole is still healthy and doing well.", "\n\nAt the conference venue.", "\n\nWhile the Manchester weather was quite challenging, the conference was well-organized and I believe we all had a lot of fun both at the conference venue and at social events, especially at the awesome GNOME 20th Birthday Party. ", "Kudos to all who made this happen!", "\n\nAt the GNOME 20th Birthday Party.", "\n\nAs I reported at the GNOME Foundation AGM, the docs team has been slightly more quiet recently than in the past and we would like to reverse this trend going forward.", "\n\nAt the GNOME 20th Birthday Party.", "\n\nWe held a shared docs and translation session for newcomers and regulars alike on the first two days of the post-GUADEC unconference. ", "I was happy to see new faces showing up as well as having a chance to work a bit with long-time contributors. ", "Special thanks goes to Kat for managing the docs-feedback mailing list queue, and Andre for a much needed docs bug triage.", "\n\nBusy working on docs and translations at the unconference venue.", "\n\nShaun worked on a new publishing system for help.gnome.org that could replace the current library-web scripts requiring release tarballs to get the content updated. ", "The new platform would be a Pintail-based website with (almost) live content updates.", "\n\nLocalization-wise, there was some discussion around language packs, L10n data installation and initial-setup, spearheaded by Jens Petersen. ", "While in gnome-getting-started-docs, we continue to replace size-heavy tutorial video files with lightweight SVG files, there is still a lot of other locale data left that we should aim to install on the user’s machine automatically when we know the user’s locale preference, though this is not quite what the user’s experience looks like nowadays. ", "Support for that is something that I believe will require more input from PackageKit folks as well as from downstream installer developers.", "\n\nThe docs team also announced a change of leadership, with Kat passing the team leadership to me at GUADEC.", "\n\nIn other news, I announced a docs string freeze pilot that we plan to run post-GNOME 3.26.0 to allow translators more time to complete user docs translations. ", "Details were posted to the gnome-doc-list and gnome-i18n mailing list. ", "Depending on the community feedback we receive, we may run the program again in the next development cycle.", "\n\nThe docs team also had to cancel the planned Open Help Conference Docs Sprint due to most core members being unavailable around that time. ", "We’ll try to find a better time for a docs team meetup some time later this year or early 2018. ", "Let me know if you want to attend, the docs sprints are open to everybody interested in GNOME documentation, upstream or downstream.", "\n\nAt the closing session.", "\n\nLast but not least, I’d like to say thank you to the GNOME Foundation and the Travel Committee for their continuous support, for sponsoring me again this year.", "\n\nThe GNOME documentation team started planning the next docs hackfest after some (rather long) months of decreased activity on that front. ", "The previous docs sprint was actually held in Cincinnati, OH, in 2015, produced lots of content updates and we’d like to repeat that experience again this year from August 14th through 16th, 2017.", "\n\nAs with the previous event, the 2017 docs sprint will happen right after the Open Help Conference, which is returning this year thanks to Shaun.", "\n\nWhat we want to do differently this year is extending invitation to all people interested in GNOME content, whether it is upstream or downstream. ", "We would especially like to see some Ubuntu folks attending. ", "With Ubuntu moving to upstream GNOME, we are already seeing an increased number of docs patches coming from Ubuntu contributors, which is great, and I think having a joint documentation event could strengthen and expand the connections even more!", "\n\nIn one of the sessions, Shaun gave a presentation onpintail, a site builder that lets you publish your documents from sources in Mallard, Ducktype, DocBook, AsciiDoc (the latter coming soon), and so on, using yelp-xsl, a package also used in GNOME Docs. ", "We are hoping to see pintail deployed in the Fedora Documentation Project soon, to replace the aging Publican-based documentation website.", "\n\nAs for the lightning talk session, I was really impressed by Eleanor Blandford and her presentation skills, given the fact that she is only 10! ", "Future GNOME hacker?", "\n\nIt was great to see GUADEC turning into a family-friendly conference. ", "Several families attended and there was a children’s corner available right at the venue.", "\n\nDuring the hackfest days, I mostly worked on squashing various documentation bugs and adding more Mallard test tokens into gnome-getting-started-docs.", "\n\nDistributors: If your distro is shipping Firefox (and not Epiphany) as the default browser, please file a bug similar to #770013 so that we can add test tokens for your distro into the getting-started page on web browsing.", "\n\nJakub and I also quickly reviewed the current SVGs and remaining getting-started videos. ", "Updates are coming in the next release! ", "With Shaun, we had a look at pintail and its support for building the Fedora DocBook-based guides.", "\n\nAs this picture says, GUADEC 2016 was well-organized and successful, so yes, thank you again organizers!", "\n\nSo I’m here in Karlsruhe, Germany attending GUADEC 2016. ", "Today was the second conference day with the GNOME Foundation AGM, which, as the tradition goes, included team reports. ", "As for L10n & docs teams, the update from the GNOME Translation Project was given by Alexandre Franke and the docs update was given by yours truly.", "\n\nIf you are at GUADEC tomorrow, don’t miss Kat’s talk Documentation: state of the union with more detailed updates on what’s been happening in GNOME docs land over the past 12 months.", "\n\nStarting Monday, we are having a GNOME docs sprint at the GUADEC BoF venue. ", "Our primary goal is to work on GNOME Help updates for the upcoming stable release but come join us even if you are not a contributing writer yet. ", "We will guide you through the writing process and gladly convert you into a successful GNOME writer!", "\n\nLast but not least, big thanks to the GNOME Foundation for sponsoring me!", "\n\nFor quite some time, lightweightdocumentationformats have been a big thing in the world of open source community documentation. ", "While corporate environments are not very eager to move from their (often) ancient documentation platforms due to cost concerns, it is usually less of an issue for a typical open source documentation project out there to migrate to a new format.", "\n\nI’ve recently started converting one of the open source documentation suites that I contribute to from a Publican-based DocBook XML source into AsciiDoc, which has been getting lots of attention especially from developer-centric communities.", "\n\nThe semantics of AsciiDoc is based on DocBook and AsciiDoc draws its roots from this industry-standard XML language. ", "This allows for an easy AsciiDoc to DocBook conversion. ", "Sadly, when you need to convert your DocBook content into AsciiDoc, you are left with a number of conversion tools which are either unmaintained or have incomplete support for DocBook syntax. ", "This is an important aspect to consider when you are planning to migrate your documentation to the new format, especially if your documentation suite is rather complex and features a rich set of syntax and semantics.", "\n\nPreparing your XML document for conversion\n\nFrom the tools available for the conversion task (pandoc + docbook2asciidoc.sh, docbook2asciidoc, and others), docbookrx seems to have the most complete support for DocBook syntax. ", "It can preserve tables, included files and images, procedures, and so on. ", "Not all DocBook elements are supported, though. ", "Here is an (incomplete) list of elements I had to replace with sed:\n\nproductname\n\nmenuchoice → menu:examplemenu[examplesubmenu > examplesubsubmenu]\n\nguimenu → [label]#example#\n\nguisubmenu → [label]#example#\n\nguimenuitem → [label]#example#\n\nuserinput → [userinput]#example#\n\noption → `example`\n\nsystemitem → `example`\n\nremark\n\nrevhistory\n\nIt is always a good idea to use a version control system to track any replacements in your XML source files.", "\n\nWhat is nice about docbookrx is that it prints a warning when it runs into an element that it can’t recognize. ", "Some of the other converters just silently drop the unrecognised element, including the content inside it, which is something to bear in mind.", "\n\nUsing docbookrx.rb\n\nClone the docbookrx repo:\n\ngit clone [email protected]:opendevise/docbookrx.git\n\nCopy the docbookrx.rb Ruby gem from the repo to the directory containing the XML files you want to convert.", "\n\nLoad the gem, specifying a root file of your document as the input file:\n\nruby docbookrx.rb Admin_Guide.xml > Admin_Guide.adoc\n\nThe gem will follow included files referenced from the root file and convert the whole document.", "\n\nRun asciidoctor to generate an HTML preview:\n\nasciidoctor Admin_Guide.adoc\n\nSome additional clean-up of your document is usually needed afterwards but the document’s overall structure and syntax should be preserved.", "\n\nThe hackfest was held at a lovely co-working place called Platform 53 in Covington, Kentucky, just across the river from downtown Cincinnati. ", "During the three intensive days full of writing, the docs team managed to update tons of pages throughout GNOME Help.", "\n\nDue to the timing of the 3.18.0 stable release, the updates, together with some updated translations, eventually landed in 3.18.1.", "\n\nI mostly focused on updating user account, power, and printing help. ", "These should be in a good shape now. ", "There are exceptions, though, like documentation on enterprise login, which is pending some code-related updates.", "\n\nSome of us struggled with getting a 3.18.0 up and running. ", "We tried different build images from GNOME Continuous, Fedora, and openSUSE. ", "While there seems to be a plenty of options at first glance, when it comes to being able to try out and preview the actual GNOME Desktop, I think there is still a long way to go.", "\n\nTesting some of the cool features in 3.18 can get challenging, for example, automatic screen brightness that requires an integrated light sensor. ", "I wish I had one!", "\n\nThe team had a profound discussion about restructuring some of the most visible topics and topic groups in GNOME Help. ", "We made good progress, although some of the issues, including content duplicity, remain unresolved. ", "Material for the next hackfest?", "\n\nAlthough this somewhat slipped through the cracks, it’s never too late to socialize the notes taken by Nuritzi Sanchez of Endless Mobile fame during the L10n-i18n-Docs BoF we ran at GUADEC 2015 (many thanks for taking them!).", "\n\nIn a nutshell, the BoF attendees, both translators and documentation writers, touched a number topics spanning from screenshot automation (a follow-up from previous year’s BoF) to onboarding, mentoring and improving the projects’ getting started material for contributors, to glossaries, style guides and similar resources.", "\n\nIf you are interested in any of those topics, please have a look.", "\n\nHope the notes can be reused as follow-ups in future i18n and/or docs meetings.", "\n\nThe area around Cincinnati has a strong German heritage, so no wonder the library also features some German manuscripts. ", "Reminds me of my years spent studying paleography.", "\n\nThe Open Help Conference is not like one of those industry conferences with large numbers of participants but the attendees here are, on the other hand, very focused on the specific topic of open source documentation and docs community management. ", "It’s always cool to see how other communities approach community docs, and learn some new tricks along the way.", "\n\nGreat to see old faces again, and meet new ones. ", "I’d like to thank the GNOME Foundation for making it possible for me to attend the conference and hackfest." ]

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[ "Incidence and risk factors for tuberculosis in HIV-infected patients while on antiretroviral treatment in Cambodia.", "\nGiven the lack of detailed studies on tuberculosis (TB) in patients on antiretroviral treatment (ART) in South-East Asia, we aimed to determine the incidence and risk factors for early (after ≤6 months of ART) and late (after >6 months of ART) incident TB in Cambodia. ", "We conducted a retrospective analysis of all patients started on ART at a non-governmental hospital in Phnom Penh (March 2003-December 2010). ", "TB diagnosis was performed according to WHO algorithms. ", "Risk factor analysis was performed using multivariate Cox regression modeling. ", "Overall, 2984 patients started ART. ", "The median baseline CD4 count was 89 cells µl(-1) (IQR 25-209), median age 34 years (IQR 29-40). ", "Fifty-three percent of the patients were female. ", "Median follow-up time on ART was 2.4 years. ", "In addition to 932 (31.2%) patients already on TB treatment at ART initiation, 313 (10.5%) developed TB, with an overall incidence rate of 3.9/100 patient-years. ", "Of those developing TB, 179 (6.0%) patients were diagnosed with early TB and 134 (4.5%) with late TB, corresponding with a rate of 13.5 and 2.0 per 100 patient-years respectively. ", "Risk factors for early TB included low body mass index, low baseline CD4 count and low hemoglobin levels. ", "Low on-treatment CD4 counts and hemoglobin levels, being underweight while on ART and prevalent TB were identified as risk factors for late TB. ", "The incidence of early TB was high, and predominantly associated with advanced HIV progression markers. ", "Earlier ART initiation and enhanced TB screening prior to and after ART initiation is warranted. ", "Late TB amounts to almost half of the total TB burden, meriting specific preventive and diagnostic approaches." ]

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[ "Story time! ", "I received this excellent parcel on Thursday. ", "I found it on the porch after an evening at the pub with my friends rewarding ourselves with many pints after a tough workout. ", "I was absolutely pissed but the sight of the parcel sobered me up quickly! ", "Or at least, sobered me up enough to remember to take pictures!", "\n\nI'm genuinely thrilled with all of it. ", "I think I actually clapped my hands when I saw the SC game :D I haven't gamed much since my son was born but I am starting to have a bit more time for that sort of thing so I'm looking forward to giving this one a go. ", "I loved the original, of course. (", "am old!)", "\n\nThe tin of G&T (behind the card in the pic) made me laugh because well, I had to go check my profile and sure enough I had wittered on about being a fan of gin. ", "The Wispa Gold HONESTLY so funny as I have been told several times recently by a friend that I need to give it a try. ", "I haven't yet but I'm expecting good things. ", "I shall make it in my new zombie killing mug, of course!", "\n\nThe Reeses has been consumed already, that never stood a chance.", "\n\nA big thanks for the inclusion of the books for my son! ", "He adores maps and flags, has recently been diagnosed as ASD so is keen on order and all that. ", "He won't open the gift yet; I peeked because I knew I'd need to report back to you! ", "Personally I agree with him and don't usually open gifts until Christmas but exceptions must be made.", "\n\nAnyway, very sorry it's taken me a few days to properly get back to you, I've actually had a social life for once and this has been my first day back in front of a screen. ", "I hope your SS treats you well, and I'll be shipping off my own parcel once the last gift arrives from Amazon..\n\nETA sorry my phone takes terrible pictures :( And so does its owner." ]

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[ "Ed: Is any one else here going to attend the ABC-USA biennial in Overland Park Kansas? ", "I would be glad to see those that we have met in other places and any of you that we have not met. ", "We will be at the Chase Suites Hotel Across the traffic circle from the Convention Center & Hotel. ", "Or my cell phone # is 518-227-5527. ", "We are making A lOOOoNG trip of it by visiting relatives in NJ, GA, Florida & Mo. We are also going to at least drive through the campus of Ouachita Baptist University in Arkansas. ", "Yea Flick that is the other OBU. ", "We are also going to take in a show or two at Branson MO. ", "on the way.", "\n\nI am looking forward to the Tour of Central Baptist Seminary that Molly has scheduled.", "\n\nCan't make it. ", "Would love to. ", "Haven't been in KS since I was a kid. ", "My main memory of it is being on the Kansas Turnpike; I was in charge of the map, and I told my dad which exit to take and he didn't believe me, and drove maybe twenty miles out of our way before he could turn around, and then he got mad at me for it. ", "I think he'd used his nasal inhaler too much that day.", "\n\nEd: Since having had breakfast with Neil last saturday, we traveled through Alabama, Mississippi, Arkansas, Missouri, to arrive in Kansas on Theursday afternoon. ", "The Chase Hotel & Suits is Luxury Plus. ", "LR?BR full Kitchen, geat bath and dressing area.", "\n\nYesterday we took a tour out to Central Seminary and Molly introduced us to a number of students, the director of the Korean program gave an overvier of the 7 programs they have operating around the country, One is in my Home town of Fort Wayne In.. Latter in the dat we took another tour to the Negro Baseball Musuem and the Jazz Musuem . ", "The opening worship servive featured AMY Butler Preaching. ", "More later. ", "1,285 registered\n\nBeing out of the loop on the ABC now, I was was just curious why the Biennial as been renamed \"Mission Summit\" and why it has be in Kansas what seems to be two years in a row? ", "Or maybe I missed the year in between? ", "But I am curious why the same location twice?", "\n\nPasadena was my last Biennial and I realize a number of things have changed in the five years I've been out.", "\n\nThe terms Biennial and Missions Conference are used pretty much interchangeably. ", "But the design has changed some from denominational politics to discussion and interchange of ideas on ways to accomplish God's mission through the local church in new less repetitive ways.", "\n\nTwo consecutive times in KC is because the Overland Park Convention Center made us a great deal for each of two years over just one. ", "Still too much packed into three days. ", "Tiring but fun. ", "Today we had 2.5 hours of small group discussions on ones choice of ONE of several aspects of local church ministry. ", "I was in a group discussing Alternative ways for churches to do ministry. ", "Trudy's group discussed discipleship methods.", "\n\nHaruo wrote:Can't make it. ", "Would love to. ", "Haven't been in KS since I was a kid. ", "My main memory of it is being on the Kansas Turnpike; I was in charge of the map, and I told my dad which exit to take and he didn't believe me, and drove maybe twenty miles out of our way before he could turn around, and then he got mad at me for it. ", "I think he'd used his nasal inhaler too much that day.", "\n\nED: Hauro: Put in your request for 2017 time off, the Biennial will be in SEATTLE. ", "Check the ABC/USA website.", "\n\n2017 Portland, not Seattle, I am told. ", "Several hundred miles difference, but I'll almost certainly be there. ", "Maybe Mrs. H. too! ", "I have a brother in Portland, so with a little luck should be able to stay for free. ", "Maybe I can get a KELI table together.", "\n\nHaruo wrote:2017 Portland, not Seattle, I am told. ", "Several hundred miles difference, but I'll almost certainly be there. ", "Maybe Mrs. H. too! ", "I have a brother in Portland, so with a little luck should be able to stay for free. ", "Maybe I can get a KELI table together.", "\n\nThanks for the correction, re; location.", "\n\nEd: The 2015 Biennial is in the books. ", "A proposed amendment to the constitution that would have more narrowly defined our view of scripture to specify 66 books and including the term infallibility, was not sent forward for consideration at the 2017 meeting. ", "No actual count was taken but from our vantage point, I would estimate the show of voting cards to have been 9 to 1. ", "The three featured Preachers for worship on Fri, Sat & Sunday where Any Butler, Roy Medley and Don NG. ", "I have heard Amy deliver more stimulating messages. ", "Roy's final Biennial Sermon as ABC/USA General Secretary was outstanding, Ng the outgoing President was well received. ", "Trudy and I attended 2 sessions of the Young Preachers Festival and heard 5 sermons. ", "All where very well done 2 where outstanding, one of the best by a young lady who just graduated from High School this spring.", "\n\nNYS was well represented with reps from the extreme, east all the way to Buffalo.", "\n\nHaruo wrote:So who's going to be Pope now that Medley has abdicated? ", "And is a new president in hand? ", "I was very happy to hear the Chin and Karen groups were successfully affiliated.", "\n\nAnd the 9 to 1, was that 9 not to send it to Portland or 9 to send it forward? ", "Where in ABC did that proposal originate?", "\n\nEd: Not to send. ", "Was I not clear about that? ", "It originated on the floor by the pastor of a church in PA that was founded in the late 1700's. ", "BTW, I voted with the majority.", "\n\nAnd Hauro, I think you needed a TIC emoticon with you question about Roy's sucessor. ", "I have never known a less Pope Like Denominational leader.", "\n\nBut in reply to the substantive part of the question the search for a replacement in the General Secretaries position has been put on hold. ", "An interim has been appointed by the General Board. ", "I do not know that persons name although it was announced from the platform.", "\n\nThe stated reason for the delay is that \"the Integrity of the search process was compromised by the leaking personal information by a member of the search committee\". ", "I was surprised to hear that this issue had not yet been resolved. ", "I have no additional details.", "\n\nAnd I was not aware that the NBC dinner was cancelled, probably not enough signed up. ", "The two or three time I passed their booth it was unmanned. ", "We are rather selective as to which breakfast or dinners we attend due to the rather exorbitant cost. ", "Our Hotel the Chase Hotel and Suites, provided a good breakfast included in the price of the room. ", "However we did attend the Historical Society breakfast. ", "ADDED at 3:30 PM Trudy just got home from the church, she says she thought she saw a sign in front of one rooms in the convention center saying that the dinner was going to be there.", "\n\nAnd Hauro I am wondering if you have a copy of a \"Negro Baptist Hymnal\" published in the early 1900's? ", "It was for sale at the Judson Press booth. ", "I may not have the exact title it may be a bit longer." ]

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[ "Inhibition of serotonin reuptake.", "\nAn uptake system on the serotonin neuronal membrane apparently functions to inactivate serotonin that has been released into the synaptic cleft. ", "Various inhibitors of this active transport system on serotonin neurons are known, and some are specific in the sense that they do not inhibit the active uptake system on norepinephrine neurons. ", "The most widely studied specific inhibitor of the serotonin neuron pump is fluoxetine, 3-(p-trifluoromethylphenoxy-N-methyl-3-phenyl propylamine (Lilly 110140). ", "When fluoxetine or other effective but less specific serotonin uptake inhibitors are given, a rapid decrease in serotonin turnover occurs and the rate of firing of single neural units in the serotonin rich raphe area of brain is reduced. ", "This decrease in serotonin turnover and release may be a compensatroy mechanism in response to an enhanced action of serotonin on synaptic receptors. ", "Through the use of fluoxetine and other serotonin uptake inhibitors, the role of serotonin neurons in various brain functions--behavior, sleep, regulation of pituitary hormone release, thermoregulation, pain responsiveness, and so on--can be studied." ]

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[ "Increasing numbers of applications are being developed in the biomedical field, which involve the use of a mechanical construct that is surgically implanted to allow the body to mend or be reconstructed. ", "These applications include spinal constructs and disk replacements, plates used for long bone repair from the femur to the metacarpals, and even soft tissue repair such as bladder and hernia repair. ", "There are even orthopedic or dental areas in which a screw is implanted by itself to hold bone in a certain position, or to provide an anchor for a dental prosthetic.", "\nOne field which is ready for product growth is small bone surgery, i.e. below the elbow and ankle. ", "Much of the work that has been done in this area in the past represents scaled down constructs and instruments from the large bone area. ", "However, many of these products are not adequate for the fine bones and delicate procedures required of the small bone surgeon. ", "These bones are fine and have minimal surface area for placement of an implant, and less mass for the placement of a screw. ", "In addition, there is usually minimal soft tissue to cover an implant. ", "These factors tend to make small bone surgery particularly tedious and unforgiving. ", "Small bone surgeons are particularly appreciative of surgical tools that provide assistance in holding, centering, and implanting the delicate screws that are used in this area of the body, especially when it means that fewer hands need to be involved in the procedure.", "\nThe present invention is designed to meet the specific needs of the small bone surgeon to facilitate effective and repeatable procedures which provide for ease of use for this specific area of specialization, although it is certainly envisioned that the screw and screw driver of the present invention could be used in a wide variety of other orthopedic and surgical applications including spinal surgery, plating in various areas of the body, soft tissue repair, and bone anchoring.", "\nThe present invention provides a screw for use alone or as part of a construct which could include a plate. ", "The screw is designed specifically for the small bone market, i.e. for use in bones distil to the elbow and knee, including, for example, the ulna, radius, tibia, fibula, as well as the metacarpals, carpals, metatarsals, tarsals, and phalanges. ", "The screw can be used in applications previously mentioned, for example those that require fixation within a single bone such as the stabilization of a fracture or the screw can be used across two or more bones so as to facilitate total or partial fusion.", "\nThe screws are advantageously, self-starting, self-tapping screws having an internal torque driving recess that terminates in a cylindrical opening or cannulation. ", "The cannulation can extend through the length of the screw or can extend only partially through the length of the screw in a partial cannula. ", "The invention further includes a screw driver having an external torque driving shape and terminating in a conical or cylindrical pilot or boss which mates with the cylindrical cannula or tapered opening in the screw. ", "The pilot is sized and held to a tolerance so as to hold the screw on the screw driver by a friction fit and further acts to center the screw's torque driving recess relative to the torque driver of the screw driver in order to help avoid stripping the torque driving recess of the driver. ", "This is a particular problem for the small screws and even smaller torque driving recesses of the screws.", "\nThe screws include an insertion end having multiple flutes, and preferably 2 or 3 flutes about a conical recess. ", "The screws further include a modified cancellous thread. ", "The screw further has a partial taper of the minor diameter of about 5° to about 15°, and more preferably about 6° to about 10°, and most preferably about 8° over about the first 2 to about 6, and more preferably about 4 complete turns of the threads adjacent to the head of the screw.", "\nThe screws further include a torque driving recess that may be a hexagon, a sinusoidal shape, or a modification of a sinusoidal (multilobed) shape. ", "This recess can be of a constant size in the direction of the longitudinal axis, or can taper inward along the longitudinal axis of the screw toward the bottom of the recess. ", "The opening for the pilot of the screw driver can be of any cross section which corresponds to the cross-section of the pilot, but circular is preferable with a taper along the longitudinal axis in one of either the pilot or the hole. ", "Thus, the pilot may have a slight taper and form an interference fit with a cylindrical opening, or alternatively and perhaps of slightly less advantage, the opening may have a slight taper and form an interference fit with a cylindrical pilot on the screw driver. ", "A cylindrical opening with a slightly tapered, i.e. about 2-5°, pilot with a flat bottom works well, and is relatively easy to manufacture in the small sizes required. ", "The driver and opening are dimensioned so that the distil end of the pilot is slightly smaller than the distil end of the opening, and the frictional fit optimally occurs right below a transition between the torque driving recess and the opening. ", "An additional feature of the recess/opening is a chamfered transition area, which could be a truncated frutoconical shape that leads from the torque driving recess into the cylindrical opening. ", "In addition, the head of the screw can include a rounded exterior portion or spherical shaped head to permit multiaxial insertion, i.e. in a corresponding rounded or spherical recess in a countersunk screw hole in a plate or other construct. ", "The screws can be provided in typical lengths for small bone use, i.e. from about 5 mm to about 25 mm and typically in lengths of 8, 12 16 and 20 mm with a major diameter of about 2.7 mm or 3.5 mm. ", "The screws can include a constant thread pitch as shown, in particular for use with a bone plate. ", "A further embodiment of the screw for use in fixation by itself is a screw which includes a compression thread which increases in the number of turns over a given length. ", "This variable pitch will preferably be used for the thread over about half of the distil end of the screw. ", "The screws can be made of appropriate biocompatible material, including for example surgical grade stainless steel and titanium. ", "The driver may be an integral design, such as stainless steel, or the pilot may be constructed as an insert for example from a more flexible material. ", "Alternatively, the pilot may be constructed as a separate and preferably retractable assembly, such as a stylet, which rejects using the same mechanism as a retractable ball point pen. ", "Preferably, the driver includes a fillet, or rounded transition between the shaft and the torque driving tip and also one between the torque driving tip and the pilot." ]

{ "pile_set_name": "USPTO Backgrounds" }

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